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- Discussion Type
- discussion topicD=6 supergravity
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicD=3 supergravity
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicD=2 supergravity
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Added pointer to today’s

Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt,

*Maximal $D=2$ supergravities from higher dimensions*[arXiv:2309.07232]Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt,

*Consistent truncation of eleven-dimensional supergravity on $S^8 \times S^1$*[arXiv:2309.07233]

- Discussion Type
- discussion topicD=5 supergravity
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicD=9 supergravity
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicD=4 supergravity Lie 2-algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

I finally realized that this ought to exist. And sure enough, it had been constructed already: the

*4d supergravity Lie 2-algebra*-extension of the 4d $N = 2$ super-Poincaré super-Lie algebra. I have added a minimum of an Idea-section and pointers to the references.

- Discussion Type
- discussion topicD=11 supergravity Lie 3-algebra
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topiccoset space structure on n-spheres -- table
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicTomotada Ohtsuki
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicknot
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by Urs
- Last Active Jul 17th 2024

I added the definition and several references on higher dimensional knots under knot.

- Discussion Type
- discussion topicBergman kernel
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jul 17th 2024

Minimal stub requested by links at reproducing kernel Hilbert space and few other entries.

- Discussion Type
- discussion topickernel method
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active Jul 17th 2024

a stub (though I did try my hand on a brief idea-section), for the moment mostly to provide a home for

- Julien Mairal, Jean-Philippe Vert,
*Machine Learning with Kernel Methods*, 2017 (pdf)

- Julien Mairal, Jean-Philippe Vert,

- Discussion Type
- discussion topictropical semiring
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by zskoda
- Last Active Jul 17th 2024

Trivial edit to start discussion.

What’s happening at the start here? We have both tropical rig and semiring defined. The latter is given with the extension by $\{\infty\}$. Is this just duplication with a mistake?

At semiring having given 4 definitions, it says

The nLab uses the second definition to define a semiring, and the fourth definition to define a rig. The first and third are then called nonunital semirings and nonunital rigs respectively.

Do we really have this as a policy?

- Discussion Type
- discussion topicMagnus expansion
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Jul 17th 2024

- Discussion Type
- discussion topiciterated integral
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by zskoda
- Last Active Jul 17th 2024

stub for

*iterated integral*(more references as soon as the nLab wakes up again…)

- Discussion Type
- discussion topicD=5 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

quick note for

*5-dimensional Chern-Simons theory*, for the moment just to record some references

- Discussion Type
- discussion topicsemi-topological D=4 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicquantization of D=3 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

added pointer to André Henriques’ recent MO comment here to

*quantization of 3d Chern-Simons theory*. Should try to find time to work that into the entry.

- Discussion Type
- discussion topicD=11 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

gave

*11d Chern-Simons theory*its own (brief, for the moment) entry (splitting off some material from*self-dual higher gauge theory*)

- Discussion Type
- discussion topicD=7 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Added a fair bit of content to

*7d Chern-Simons theory*.Of the three examples discussed there, the first two are review. The third is inspired by something I have been talking about with D. Fiorenza, C. Rogers and H. Sati.

- Discussion Type
- discussion topicD=6 Chern-Simons theory
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”.)

- Discussion Type
- discussion topicD=4 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

started adding these kinds of references, but maybe this should eventually go in its own stand-alone entry:

A kind of 4d Chern-Simons theory intermediated between ordinary 3d Chern-Simons theory and compled 3d (hence real 6d) holomorphic Chern-Simons theory:

Kevin Costello, Edward Witten, Masahito Yamazaki,

*Gauge Theory and Integrability, II*, ICCM Not. 6, 120-146 (2018) (arXiv:1802.01579)Kevin Costello, Edward Witten, Masahito Yamazaki,

*Gauge Theory and Integrability, I*, ICCM Not. 6, 46-119 (2018) (arXiv:1709.09993)Meer Ashwinkumar, Meng-Chwan Tan, Qin Zhao,

*Branes and Categorifying Integrable Lattice Models*(arXiv:1806.02821)

- Discussion Type
- discussion topicD=3 Chern-Simons theory
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”)

- Discussion Type
- discussion topicD=1 Chern-Simons theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicD=2 Chern-Simons theory
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”)

- Discussion Type
- discussion topicE₈ manifold
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Added to fix a dead link.

- Discussion Type
- discussion topicE₈ lattice
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicSpin(8)-subgroups and reductions -- table
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicgeneralized G₂-manifold
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicWilhelm Magnus
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jul 17th 2024

Discovering so called Magnus expansion, as an application of Lie theory to differential equations,

- Wilhelm Magnus,
*On the exponential solution of differential equations for a linear operator*, Commun. Pure Appl. Math.**7**:4 (1954) 649–673 (1954) doi

- Wilhelm Magnus,

- Discussion Type
- discussion topicSpin(7)/G₂ is the 7-sphere
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

for completeness, to go with the other entries in

*coset space structure on n-spheres – table*

- Discussion Type
- discussion topicM-theory on G₂-manifolds
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

started

*M-theory on G2-manifolds*

- Discussion Type
- discussion topicG₂/SU(3) is the 6-sphere
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicG₂-orbifold
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “G2-orbifold” from the top and added one for “G2-orbifold” at the bottom of the page.)

- Discussion Type
- discussion topicG2-conifolds -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

starting something (a bare list of references, to be

`!include`

ed into relevant entries, such as at*G2-manifold*and*conical singularity*)

- Discussion Type
- discussion topicG₂-conifold
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicG₂-MSSM
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

As a welcome means of procrastinating work on

*spectral sequence*, I created*G2-MSSM*and touched or created stubs for a bunch of related entries, such as adding references to*G2-manifold*, creating*model (in particle physics)*, disambiguating at*model*etc. pp.

- Discussion Type
- discussion topicG₂ manifold
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicU-duality -- table
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

- Discussion Type
- discussion topicE₇
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

added to

*E7*the statement of the decomposition of the smallest fundamental rep under $SL(8,\mathbb{R})$ and $SL(7,\mathbb{R})$ (here) and used this then to expand the existing paragraph on*As U-duality group of 4d SuGra*

- Discussion Type
- discussion topicG₂
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

added to

*G2*the definition of $G_2$ as the subgroup of $GL(7)$ that preserves the associative 3-form.

- Discussion Type
- discussion topicE₁₁
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

have added a minimum on the level decompositon of the first fundamental rep of $E_{11}$ here.

- Discussion Type
- discussion topicE₁₀
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “E10” from the top and added one for “E10” at the bottom of the page.)

- Discussion Type
- discussion topicE₉
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Added redirect for “E9” at the bottom of the page.)

- Discussion Type
- discussion topicE₈
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

added statement of and references for some of the homotopy groups of $E_8$ to E8

- Discussion Type
- discussion topicE₆
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

expanded

*E6*a bit.

- Discussion Type
- discussion topicF₄
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Jul 17th 2024

added some references on representationology of $F_4$ to

*F4*

- Discussion Type
- discussion topicambidextrous adjunction
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by varkor
- Last Active Jul 17th 2024

started a stub for

*ambidextrous adjunction*, but not much there yet

- Discussion Type
- discussion topicRenzo L. Ricca
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2024

- Discussion Type
- discussion topicoriented link
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2024

- Discussion Type
- discussion topicFox's theorem
- Category Latest Changes
- Started by J-B Vienney
- Comments 6
- Last comment by J-B Vienney
- Last Active Jul 16th 2024

- Discussion Type
- discussion topicAlejandro Díaz-Caro
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2024

- Discussion Type
- discussion topicquantum lambda-calculus
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jul 16th 2024

- Discussion Type
- discussion topicreflexive graph
- Category Latest Changes
- Started by RodMcGuire
- Comments 4
- Last comment by Urs
- Last Active Jul 16th 2024

I’ve added to reflexive graph a definition of the free category of a reflexive quiver.

That page needs some reorganization because everything now said there is about reflective quivers, and not say about reflective undirected simple graphs.

Maybe free category also also needs touching up and maybe a link to reflective graph. I don’t know how to justify that the paths in the free category don’t contain identity edges.

- Discussion Type
- discussion topic2-category with contravariance
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by varkor
- Last Active Jul 16th 2024

Created 2-category with contravariance and 3-category with contravariance, combining ideas from this preprint of mine with ideas that Vladimir Sotirov had written at contravariant functor (which I moved from there to here).

- Discussion Type
- discussion topicgeneralized multicategory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by varkor
- Last Active Jul 16th 2024

There is a student here who is thinking about how to relate $\infty$-algebraic theories with $\infty$-operads and in the course of that also dendroidal sets with Lurie-type “$\infty$-categories of operations” of $\infty$-operads.

I am trying to help a bit where I can. First of all I thought I’d need to get a better idea of how the triangle

$\array{ && monads \\ \\operads &&&& algebraic theories }$

works in 1-category theory. So I am naturally looking at Mike’s

*Generalized Virtuology*to get some hints.I had planned to typeup the little that I understand about the relation between Lawvere theories and generalized multicategories, but now I ended up spending some time just on the entry on virtual double categories. Here is what I did

created a subsection “Monads on virtual double categories” with the basic definitions

and further subsections on “Monoids and modules” (this existed as an empty stub before)

and “Generalized multicategories” (with the basic definition, then pointing over to generalized multicategory of course).

I also

created vDbl

added the raw definition and the reference and virtual equipment.

I took the liberty of mentioning the term “fc-multicategory” at the beginning of virtual double category (because that happens to remind me easier of what the term refers to) and at virtual equipment I said that this term is short for “proarrow equipment of a virtual double category”.

(Hm, that summary of what i did is almost longer than the little bit of text that I acutally added! :-)

Mike, here is a question:

when I read your article with Cruttwell, I have slight trouble when it comes to definition 8.2 of normalized monoids. It has a horizontal morphism labeled $U_A$ where definition 4.2 has an equality. It seems. Is there a typo in one of these or did I miss some further definition in the intermediate four sections (not unlikely)?

- Discussion Type
- discussion topicstructured category
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active Jul 16th 2024

Added a cross-reference to representable multicategory. It may be worth merging this page with that one.

- Discussion Type
- discussion topicempirical mean
- Category Latest Changes
- Started by PaoloPerrone
- Comments 1
- Last comment by PaoloPerrone
- Last Active Jul 15th 2024

- Discussion Type
- discussion topiclaw of large numbers
- Category Latest Changes
- Started by PaoloPerrone
- Comments 1
- Last comment by PaoloPerrone
- Last Active Jul 15th 2024

- Discussion Type
- discussion topicergodic decomposition theorem
- Category Latest Changes
- Started by PaoloPerrone
- Comments 1
- Last comment by PaoloPerrone
- Last Active Jul 15th 2024