In an applied research problem I am currently working on, I am using non-commutative semiring convolution to formulate some interesting types of calculations on images and solid ob …

Let $G$ be a Lie group and let $H$ be a closed subgroup of $G$. Then $G/H$ may not be a group, but it will be a homogeneous space for $G$ with stabilizers conjugate to $H$. Somet …

There were errors in the way I framed the question last time. So doing a major revision this time. Consider $SU(2)$ as a homogeneous space $SU(2)\times SU(2)/SU(2)$ and section …

This question is related to a previous question of mine. More specifically, it results from my attempts to understand the simplest incarnation of a phenomenon mentioned therein. P …

Actually, my question is a bit more specific: Does every complex semisimple Lie group $G$ admit a faithful finite-dimensional holomorphic representation? [As remarked by Brian Conr …

Cartan's theorem states that any topologically closed subgroup of a Lie group is an embedded Lie subgroup. This leads us to ask the following question: Can we replace "topolog …

Given the group SU(N) of NxN unitary matrices, does there exist a subgroup S with a manifold dimension larger than the SU(N-1) manifold dimension and smaller than the SU(N) one? S …

I've been looking at an example in the non-commutative geometry literature and I'm having trouble figuring out what the classical motivation is. I'll just describe the classical ca …

Let $G$ be a (maybe Lie) group, and $M$ a space (perhaps a manifold). Then a principal $G$-bundle over $M$ is a bundle $P \to M$ on which $G$ acts (by fiber-preserving maps), so t …

Bert Kostant mentioned an odd fact to me some time ago. As usual (with such statements), fix a complex, connected, reductive) Lie group $G$, with maximal torus $T$, and Weyl vecto …

I'm trying to learn about moment maps in symplectic topology (suppose our Lie group is G with lie algebra g, acting on the symplectic manifold (M,w) by symplectomorphisms). I'm hav …

Can there exist two non-equivalent equivariant actions of a group $G$ on vector bundle over a $G$ space?

Consider the metric space on, say, ℝ2 induced by the various $L^p$ norms, and the group of isometries from that space into itself that preserve the origin. When $p=2$ I get t …

I find Wikipedia's discussion of symbols of differential operators a bit impenetrable, and Google doesn't seem to turn up useful links, so I'm hoping someone can point me to a more …

I was inspired by the following algebraic topology orals question: "Is $S^1$ the loop space of another space?" This is easy to see if you recognize that $S^1$ is a $K(\mathbb{Z}, …