A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP

Year 2018, Volume: 24 Issue: 24, 68 - 72, 05.07.2018

Markus Linckelmann

https://doi.org/10.24330/ieja.440216

Cited By: 1

Abstract

By results of Boltje and Kulshammer, if a source algebra A of a

principal p-block of a nite group with a defect group P with inertial quotient

E is a depth two extension of the group algebra of P, then A is isomorphic

to a twisted group algebra of the group P o E. We show in this note that

this is true for arbitrary blocks. We observe further that the results of Boltje

and Kulshammer imply that A is a depth two extension of its hyperfocal

subalgebra, with a criterion for when this is a depth one extension. By a

result of Watanabe, this criterion is satised if the defect groups are abelian.

Keywords

Source algebra

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