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Results tagged with gr.group-theory
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user 3927
Questions about the branch of algebra that deals with groups.
32
votes
What is the difference between PSL_2 and PGL_2?
As Kevin says, the "right" definition of ${\rm{PSL}}_n$ is as representing the quotient sheaf ${\rm{SL}}_n/\mu_n$, just as one defines ${\rm{PSO}}(q) = {\rm{SO}}(q)/Z_{{\rm{SO}}(q)}$ (with $Z_G$ denot …
- 7,108
19
votes
Is a quotient of a reductive group reductive?
It is important in answering this question that one can extend scalars to a perfect (e.g., algebraically closed) ground field, as was implicit in many of the other answers even if not said explicitly. …
- 7,108
10
votes
Unipotent linear algebraic groups
Let U be a smooth connected unipotent group over an arbitrary field k, and let T be a k-split k-torus equipped with a left action on U such that the T-action on Lie(U) contains no occurrence of the tr …
- 7,108
7
votes
Algebraic groups of relative rank 1
Assume $n \ge 5$ to avoid interference with exceptional isomorphisms among small Dynkin diagrams. The case of odd $n$ should be easier, since in that case (with $n \ge 5$) there are no nontrivial dia …
- 7,108