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Results tagged with lie-groups
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user 16702
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
10
votes
Accepted
Relationship between Laplacian and Hessian on compact Lie groups
This has nothing to do with Lie groups, I believe. Let $M$ be a Riemannian manifold. The Bochner formula on $1$-forms states that
$$\nabla^* \nabla \omega = (d \delta + \delta d)\omega - \mathrm{Ric}\ …
- 9,853
3
votes
1
answer
76
views
Non-invariant forms on loop Lie algebra of semisimple Lie group
Let us consider a Lie group $G$ with Lie algebra $\mathfrak{g}$ and let $L\mathfrak{g} = C^\infty(S^1, \mathfrak{g})$ the Lie algebra of the loop group $LG$.
My question is about continuous Lie algebr …
- 9,853
1
vote
Accepted
Non-invariant forms on loop Lie algebra of semisimple Lie group
Thanks to Yves Cornulier, for suggesting to look at the paper of Neeb and Wagemann. After reading Example 6.2 of that paper (arxiv version), I think the answer to my question is that in fact all 2-cyc …
- 9,853