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

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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 Mathematics, Computer Science & Engineering
URI: http://openaccess.city.ac.uk/id/eprint/6903

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