Linckelmann, M. (2018). A note on the depth of a source algebra over its defect group. International Electronic Journal of Algebra, 24, pp. 6872. doi: 10.24330/ieja.440216
Abstract
By results of Boltje and Külshammer, if a source algebra A of a principal pblock 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 Mathematics, Computer Science & Engineering > Mathematics 
URI:  http://openaccess.city.ac.uk/id/eprint/20246 

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