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Results tagged with algebraic-groups
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user 13139
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
2
answers
1k
views
Connectedness of Centralizers in $GL_n$
I was wondering if there is any obvious reason or quick proof that for every $g\in GL_n$ the centralizer $Z_{GL_n}(g)$ is connected. Also I wanted to see why for any semisimple $s\in Sp_{2n}$ the cen …
- 2,108
2
votes
2
answers
539
views
The product of non-commuting semisimple matrices need not be semisimple
In general when one proves that the product of semisimple (i.e. diagonalizable) matrices is semisimple one assumes they commute and are thus simultaneously diagonalizable, and then the result follows. …
- 2,108