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    • at Peierls bracket I have added a bunch of further references and have slightly expanded the Idea-section

    • I have now what should be a readable pre-version of

      This still needs a round of polishing or two. But it should be at least readable.

      If anyone is interested, have a look, be critical and try to poke holes into it.

    • Changed the page local section to discuss a slightly more general concept than the local sections of a bundle, and over a more general pretopology.

    • added some references on representationology of F 4F_4 to F4

    • had need for a small table worldvolume-target supersymmetry of brane sigma-models and so I created one. Have included it into the relevant entries.

      Also created a stub for superembedding approach, the middle entry of the table.

      (An nForum issue: as of late I get to see the nForum only in its plain HTML-form, which is very inconvenient. Is this a problem just on my side, or does anyone else experience this?)

    • As we were discussing profinite completions the other day in another thread I thought I would add in some points about completed group algebras at profinite group and add some mention of pseudo compact algebras to the pre-existing entry on pseudocompact rings.

      It is not clear to me what the connection between these algebras and profinite algebras should be. These pseudocompact and related linear compact algebras use finite dimensionality instead of finiteness to get a sort of algebraic compactness condition.

    • I have Polchinski’s textbook a category:reference-entry String theory, for purposes of better linking to it

    • added little bit more to super translation Lie algebra, including a remark that it is a central extension of the superpoint, regarded as an abelian super Lie algebra.

    • I only noticed now that the discussion around equation (2.14) in

      • Ling Bao, Viktor Bengtsson, Martin Cederwall, Bengt Nilsson, Membranes for Topological M-Theory (arXiv:hep-th/0507077)

      identifies the exceptional super Lie algebra (2+2)(2+2)cocycle on 𝔰𝔦𝔰𝔬(7)\mathfrak{siso}(7) (given by the brane scan) with the “topological membrane” of “topological M-theory”.

      I added a brief remark to this extent to topological membrane and updated brane scan accodingly. Hope to be expanding on this soon…

    • I created a small page for compact symplectic group, which is not the same as the symplectic group, and added some sentences at both to disambiguate. I’m also working on an entry orthogonal group of an inner product space, which will give the general treatment that covers O(n)O(n), U(n)U(n) and Sp(n)Sp(n) (and other cases of mixed signature, like O(n,m)O(n,m)).

      There are interesting charts for O(n,𝕂)O(n,\mathbb{K}) using its Lie algebra (in fact various tangent spaces) which don’t come from the exponential mapping, and my aim is to get a reasonably full treatment of these in there.

    • started an index at Elephant

      just a tiny beginning. we have entries for many keywords already.

    • I have added to microcausality a quote with a nice discussion. That also cites experimental bounds. But back from the 1970s only – there must be better ones by now.

      Does anyone happen to know a citation for better experimental bounds, or else might anyone enjoy googling for it? I am out of googlin time now, but I am entertaining myself with advertizing this as an “experimental bound on higher category theory in fundamental physics”, along the lines of the story here.

    • At partition, I've defined partitions of sets, numbers, intervals, measure spaces, and unity on topological spaes, giving these all as special cases of a general concept defined in a monoid whose nonzero elements form an ideal (and possibly equipped with some notion of infinite sum).

    • lightning remark here on Willwacher’s identification of the GT Lie algebra with H 0H^0 of the graph complex

    • I wrote up a brief little note on this on my web. Comments are very welcome. This could be transported to the nLab if one wants.

    • surprised that we didn’t have this “people”-entry before, now we do: Kuo Tsai Chen

    • created amenable topological groupoid. Skipped the definition (gave a pointer, though), just wanted to quickly record that the convolution algebras of amenable groupoids are in the bootstrap category. Added that proposition also there.

    • Created modelizer. It’s not clear to me exactly what Grothendieck is taking as a property or as a structure in his definitions, but I tried to make a guess.

    • An updated version of the book J-holomorphic Curves and Quantum Cohomology can be found on the web page of Dusa McDuff which is linked at the new entry Dusa McDuff ! I also started a stub symplectic topology and just a little longer one for Floer homology.

    • created Dirac induction with a brief note on the relation to the orbit method, via FHT-II.

    • I started a page about the simplicial bar construction. I haven’t checked all the details carefully (especially regarding 𝒱\mathcal{V}-naturality!) though.

    • added a brief remark to discrete object in a new section Examples — in infintiy-toposes on the relation between discreteness and cohomology.

      This is a (fairly trivial) comment on Mike’s discussion over on the HoTT blog, linked to from the above.

    • I decided to add some content to the motivic pages here on the nLab.

      I started with Nisnevich site. More to come soon…

    • trivia, but I just ran into this:

      I noticed we have entries:


      both of them referring to operator algebraists. First I thought we need to merge these entries. But after looking around I guess these are indeed two different people. (The German Wikipedia claims here that the second initial of the author of K-Theory for Operator Algebras is “E” not “A”).

      (Notice that the second entry is mistaken, where it says “Home page” it points not to some author’s home page but to the nLab home page…)

      Just making sure. Sorry for the distraction.

    • I was starting to make some notes on the new article by Sergei Gukov and Anton Kapustin, at a new “reference”-categorized entry titled

      Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories

      But so far there is just a vague indication of the main thrust. I want to flesh out more detail later. On the other hand, tomorrow morning I’ll be going on a two week vacation, so this plan will encounter delays.

    • For the sake of illustration I have added to ordinary homology a section In terms of higher linear algebra.

      Currently the main point is to record, after some preliminaries, the standard observation plus detailed proof that for XX a topological space, its ordinary chain complex of singular simplices is, up to equivalence, the \infty-colimit of the tensor unit local system with coefficients in HkModH k Mod. (Its “HkHk-Thom spectrum”.)

    • In the section compacta as algebras, I have written out complete details of a proof that compact Hausdorff spaces are monadic over sets.

    • concerning stable map: is there some nice abstract characterization? Something involving maybe the words “faithful functor of étale groupoids”?