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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 …
Mikola's user avatar
  • 2,392
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 …
Mikola's user avatar
  • 2,392
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 …
Mikola's user avatar
  • 2,392
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 …
Mikola's user avatar
  • 2,392
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 …
Mikola's user avatar
  • 2,392