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I'm curious about the beautiful descriptions of exceptional simple complex Lie groups and algebras (and maybe their compact forms). By beautiful I mean: simple (not complicated - it means that we need ...

In great generality a Lie group mod its maximal compact subgroup is contractible (for example this is true for all connected Lie groups). Whenever this is true then the Lie group $ D $ is ...

On MSE this got 5 upvotes but no answers not even a comment so I figured it was time to cross-post it on MO: Is the Moebius strip a linear group orbit? In other words: Does there exists a Lie group $ ...

Let $G$ be a Lie group and $R$ be the largest connected solvable normal subgroup of $G$. Question 1 Is there a Lie subgroup $S$ such that: (1) $G=SR$; (2) every real representation of $S$ is ...