On symmetric quotients of symmetric algebras

Kessar, R., Koshitani, S. & Linckelmann, M. (2015). On symmetric quotients of symmetric algebras. Journal of Algebra, 442, pp. 423-437. doi: 10.1016/j.jalgebra.2014.05.035

Abstract

We investigate symmetric quotient algebras of symmetric algebras, with an emphasis on finite group algebras over a complete discrete valuation ring O. Using elementary methods, we show that if an ordinary irreducible character χ of a finite group G gives rise to a symmetric quotient over O which is not a matrix algebra, then the decomposition numbers of the row labelled by χ are all divisible by the characteristic p of the residue field of O.

Publication Type:	Article
Additional Information:	© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Symmetric algebra; Finite group
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology