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I have a compact connected Lie group $G$ with Lie algebra $\mathfrak{g}$ and a codimension one closed subgroup $H$ with Lie algebra $\mathfrak{h}$. Using an inner product on $\mathfrak{g}$ one can the …

So, my question specifically pertains to $T^*SO(3)$ but I guess adjusted it could be asked about Lie groups in general. The canonical symplectic form on the cotangent bundle is invariant under the cot …

Let $\rho$ be a group action by a compact group $G$ \begin{equation} \rho:G\times M \rightarrow M \\ \rho:(g,p) \rightarrow \rho_g(p) \end{equation} Denote the orbit of $p\in M$ by $\mathca …

An integrable system can be defined as a symplectic manifold together with the maxiumum possible number of Poisson commuting functions on the manifold which are almost everywhere independent. By the L …

In particular, I am wondering if $H^1_{DR}(G)\neq 0$ implies that the group can written as a semidirect product of $\mathbb{S^1}$ and something else, with the $\mathbb{S^1}$ factor being responsible f …

I have a bit of a contradiction in my brain and I was hoping once again that excellent Mathoverflow community could help me out :) Let $\rho_g$ be the action associated to a non-abelian Lie Group $G$ …

I posted this on stack exchange but had no joy, perhaps someone here can answer : The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group …