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Results tagged with lie-groups
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user 3927
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
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
18
votes
Are complex semisimple Lie groups matrix groups?
In the spirit of the title of the question, the argument doesn't quite prove that $G$ is a matrix group, since more input is needed to prove that the faithful representation has closed image which is …
- 7,108
74
votes
Classification of (compact) Lie groups
Compact Lie groups may not be connected, and the question did not assume connectedness whereas all of the other answers did. If $G$ is a linear algebraic group over $\mathbf{R}$ then $G(\mathbf{R})$ …