Graded semisimple algebras are symmetric
Rings and Algebras
2017-07-24 v2
Abstract
We study graded symmetric algebras, which are the symmetric monoids in the monoidal category of vector spaces graded by a group. We show that a finite dimensional graded semisimple algebra is graded symmetric. The center of a symmetric algebra is not necessarily symmetric, but we prove that the center of a finite dimensional graded division algebra is symmetric, provided that the order of the grading group is not divisible by the characteristic of the base field.
Cite
@article{arxiv.1504.04868,
title = {Graded semisimple algebras are symmetric},
author = {Sorin Dascalescu and Constantin Nastasescu and Laura Nastasescu},
journal= {arXiv preprint arXiv:1504.04868},
year = {2017}
}