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

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International Electronic Journal of Algebra
Volume:24 Issue:24
A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP

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

Pages : 68-72

View : 11 | Download : 9

Publication Date : 2018-07-05

Article Type : Research Paper

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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