On weakly complete group algebras of compact groups
Group Theory
2019-11-18 v4 Operator Algebras
Rings and Algebras
Abstract
We study group algebras for compact groups in the category of real and complex weakly complete vector spaces. We also show that the group algebra is a quotient of the weakly complete universal enveloping algebra of the Lie algebra of the compact group. We relate this to Tannaka duality, and to functorial properties of the group algebra. We determine the structure of the group algebra in terms of the irreducible representation, both in the real and the complex case. The particular case of a compact abelian group is worked out in detail.
Keywords
Cite
@article{arxiv.1904.00806,
title = {On weakly complete group algebras of compact groups},
author = {Karl Heinrich Hofmann and Linus Kramer},
journal= {arXiv preprint arXiv:1904.00806},
year = {2019}
}
Comments
v1, 2 appeared as an Oberwolfach Preprint. v3 considerably expanded and extended. v4 final version, to appear in Journal of Lie Theory