Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Cartan matrix of a group algebra modulo any power of its radical


Author: Peter Landrock
Journal: Proc. Amer. Math. Soc. 88 (1983), 205-206
MSC: Primary 20C05; Secondary 16A26
MathSciNet review: 695241
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Abstract: We prove that the Cartan matrix of a group algebra $ F[G]$ modulo any power of its radical $ J$ is dual symmetric, provided $ F$ is a splitting field of $ F[G]/J$. This eases the process of determining the Loewy series of the projective indecomposable $ F[G]$-modules.


References [Enhancements On Off] (What's this?)

  • [1] Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. MR 0144979

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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0695241-2
Article copyright: © Copyright 1983 American Mathematical Society