created a table-for-inclusion

and included it into relevant entries

]]>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*

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

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

]]>expanded *E6* a bit.

added some references on representationology of $F_4$ to *F4*

added some references to *group completion*, in particular Quillen’s “appendix Q”. More should be added, though.

I have split off spin^c from spin^c structure

]]>started *Bruhat decomposition*, so far just the plain definition

the same paragraph I also included at *Schubert calculus*

the entry *[[group algebra]]* had been full of notation mismatch and also of typos. I have reworked it now.

added a table with some homotopy groups in the unstable range to *orthogonal group – Homotopy groups*

added a chunk of some standard basics to *elliptic curve – Definition over a general ring*.

Also touched/briefly created various related entries, such as *Weierstrass equation*, *Weierstrass elliptic function*, *cubic curve*, *j-invariant* etc.

added to [[group cohomology]]

in the section structured group cohomology some remarks about how to correctly define Lie group cohomology and topological group cohomology etc. and how not to

in the section Lie group cohiomology a derivation of how from the right oo-categorical definition one finds after some unwinding the correct definition as given in the article by Brylinski cited there.

it's late here and I am now in a bit of a hurry to call it quits, so the proof I give there may need a bit polishing. I'll take care of that later...

]]>Added to *Klein geometry* a section *History* with quotations for where exactly Klein actually speaks about $G/H$.

(This key passages is a bit hidden in Klein’s text, appearing at a somewhat unexpected point somewhere in the middle of a 35 page document.)

]]>added to group extension a section on how group extensions are torsors and on how they are deloopings of principal 2-bundles, see group extension – torsors

]]>created a bare minimum at *jet group*

have now spelled out at *Tor* in simple terms how $Tor_1^{Ab}(A,B)$ is a torsion group, so far for the case that $A$ is finite.

I noticed that there was no entry *quotient stack*, so I quickly started one, just to be able to point to it from elswhere.

for completeness, I created a stub for *direct product group*. In the course of this I noticed that at *Cartesian product* no other example than products of sets were mentioned. So I added pointer to *direct product group* and to *product topological space*. Much more should be added.

added a minimum to *Lorentz group*.

at *additive functor* there was a typo in the diagram that shows the preservation of biproducts. I have fixed it.

Also formatted a bit more.

]]>stated a kind of Idea/definiton at *motivic Galois group*.

Experts and experts-to-be, please check!

]]>added some very basic facts on $SU(2)$ here to *special unitary group*. Just so as to be able to link to them.

for ease of linking I gave *fundamental theorem of finitely generated abelian groups* a stubby entry of its own.

In the course of this I also created a stub for *structure theorem for finitely generated modules over a principal ideal domain* which used to be requested at *principal ideal domain*.

had added to *finite group* two classical references, Atiyah on group cohomology of finite groups, and Milnor on free actions of finite groups on $n$-spheres.

What I’d really like to know eventually is the degree-3 group cohomology with coefficients in $U(1)$ for the finite subgroups of $SO(3)$.

]]>