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A note on the depth of a source algebra over its defect group

Linckelmann, M. (2018). A note on the depth of a source algebra over its defect group. International Electronic Journal of Algebra, 24, pp. 68-72. doi: 10.24330/ieja.440216


By results of Boltje and Külshammer, if a source algebra A of a principal p-block of a finite 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 ⋊ E. We show in this note that this is true for arbitrary blocks. We observe further that the results of Boltje and Külshammer 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 satisfied if the defect groups are abelian.

Publication Type: Article
Publisher Keywords: Source algebra, depth
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
Text - Published Version
Available under License Creative Commons: Attribution International Public License 4.0.

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