Semisimplicity of certain representation categories
Quantum Algebra
2015-09-08 v1 Representation Theory
Abstract
We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence of a Peter-Weyl decomposition of the corresponding sub-bimodule. Finally, we use this technique to establish the semisimplicity of certain finite-dimensional representations of the quantum double of sl_2 for generic q.
Cite
@article{arxiv.1509.01633,
title = {Semisimplicity of certain representation categories},
author = {John E. Foster},
journal= {arXiv preprint arXiv:1509.01633},
year = {2015}
}
Comments
37 pages, 3 figures