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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
78
votes
12
answers
12k
views
Why aren't representations of monoids studied so much?
It seems to me like every book on representation theory leaps into groups right away, even though the underlying ideas, such as representations, convolution algebras, etc. don't really make explicit u …
18
votes
1
answer
3k
views
What problem do the adeles solve?
While browsing through some papers, I came across some literature discussing the Arthur-Selberg trace formula. At a conceptual level I think I understand what it is doing, but when I get down to the …
7
votes
3
answers
2k
views
Which Riemannian manifolds admit a finite dimensional transitive Lie group action?
This is a basically an adjusted version of my earlier question about how to define a convolution algebra on a general Riemannian manifold. The motivation for asking such a question of course comes fr …
4
votes
2
answers
629
views
Bits and orbits
I know this title makes what I am about to ask sound like an off topic CS theory question but please bear with me because I assure you that it is not! (Well mostly, actually I am about ~90% certain th …
5
votes
0
answers
513
views
Generalized Haar Measures and Semiring-Valued Integrals on Lie Groups
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 objects. For discrete …