On diagonal entries of Cartan matrices of p-blocks
Yoshihiro Otokita
TL;DR
This paper investigates inequalities related to Cartan matrices, centers, and socles of blocks in group algebras, extending known results on Reynolds ideals to broader contexts.
Contribution
It generalizes existing facts about Reynolds ideals to new inequalities involving Cartan matrices, centers, and socles of group algebra blocks.
Findings
Derived inequalities for Cartan matrices of p-blocks
Extended understanding of centers and socles in block theory
Generalized dimension results for Reynolds ideals
Abstract
In this short note, we show some inequalities on Cartan matrices, centers and socles of blocks of group algebras. Our main theorems are generalizations of the facts on dimension of Reynolds ideals.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · graph theory and CDMA systems