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Results tagged with algebraic-groups
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user 138629
Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.
3
votes
3
answers
1k
views
Nilpotent elements of Lie algebra and unipotent groups
Let $k$ be a field of characteristic 0 (not necessarily algebraically closed), let $G$ be a connected split reductive group over $k$ and let $\mathfrak{g}$ be the Lie algebra of $G$.
Let $X \in \mat …
- 123
1
vote
1
answer
184
views
Relative position and change of torus
Let $G$ be a connected split reductive group over a field $k$ of characteristic $0$. Let $T$ and $T'$ be two split maximal tori of $G$ and $B \supset T, B' \supset T'$ be two Borel subgroups of $G$.
…
- 123
1
vote
Relative position and change of torus
I finally found a solution to my own question :
Let $g \in G$ be such that $gTg^{-1} = T'$ and $gwBw^{-1}g^{-1} = B'$. Let $b \in B$ be as in the question i.e. it verifies $bB'b^{-1} = wBw^{-1}$. We …
- 123