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Dec
21 |
comment |
Integral cohomology of elementary abelian groups
Thanks! Indeed, one proceeds inductively: this is clearly true for $n=1$, the exact sequence in the Künneth formula splits, and all $Tor$ groups are elementary Abelian in this case. |
Dec
21 |
asked | Integral cohomology of elementary abelian groups |
Mar
19 |
awarded | Nice Answer |
Sep
22 |
asked | Outer group automorphisms preserving conjugacy classes of pairs of commuting elements |
Sep
22 |
awarded | Autobiographer |
May
3 |
awarded | Necromancer |
Mar
6 |
comment |
Outer automorphisms of Borel subgroup
Thanks, Aakumadula ! Probably one can deduce that $\theta$ (modulo an inner automorphism) respects root subgroups by using that normal abelian subgroups of $B$ are in bijection with positive roots (at least for the type $A_n$). In particular, maximal normal abelian subgroups of $B$ correspond to simple roots. The automorphism $\sigma'$ of $B$ given by composition of taking transpose w.r.t (1n) -- (n1) diagonal and taking the inverse. Does this coincide with your $\sigma$? (it corresponds to the symmetry of the $A_n$ Dynkin diagram). |
Mar
5 |
comment |
Outer automorphisms of Borel subgroup
Thanks! Sure $B$ coincides with its normalizer in $GL(n, F)$. But it appears that there are non-trivial outer automorphisms of $B$ , e.g., coming from automorphisms of $F$. Also, in this paper deepblue.lib.umich.edu/handle/2027.42/30473 the group $Out(B)$ is computed when $F$ is the field of $2$ elements. It is surprisingly large (in this case, of course, $B$ is the group of unipotent upper-triangular matrices) |
Mar
5 |
revised |
Outer automorphisms of Borel subgroup
added 11 characters in body |
Mar
5 |
revised |
Outer automorphisms of Borel subgroup
edited body |
Mar
5 |
comment |
Outer automorphisms of Borel subgroup
Hi Jon! nice to see you here. |
Mar
5 |
awarded | Student |
Mar
5 |
asked | Outer automorphisms of Borel subgroup |
Jan
6 |
awarded | Yearling |
Jun
2 |
awarded | Critic |
May
29 |
answered | Semisimple Hopf algebras with commutative character ring |
May
28 |
answered | Monoidal structures on von Neumann algebras |
May
28 |
awarded | Editor |
May
28 |
revised |
Non-symmetric Braiding on finite group Representation Categories
deleted 106 characters in body |
May
28 |
comment |
Non-symmetric Braiding on finite group Representation Categories
Victor is right. I will edit the above answer. |