Graded semisimple algebras are symmetric

2015/04/19 by Dascalescu, Sorin, Nastasescu, Constantin, Nastasescu, Laura · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1504.04868

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.

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• Commonly Graded Algebras and Their Homological Properties

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