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Morita equivalent blocks in Clifford theory of finite groups. (English) Zbl 0725.20006

Représentations linéaires des groupes finis, Proc. Colloq., Luminy/Fr. 1988, Astérisque 181-182, 209-215 (1990).
[For the entire collection see Zbl 0699.00023.]
Let F be an algebraically closed field of characteristic \(p>0\) and K be a normal subgroup of a finite group H, let B be a block (subalgebra) of FK and A be a block of FH covering B, i.e. \(1_ A1_ B\neq 0\). A and B are called “naturally Morita equivalent”, if there exists a simple F- subalgebra S of A such that the algebra \(1_ AB\otimes_ FS\) is naturally isomorphic to A. The author gives necessary and sufficient conditions for this type of Morita equivalence.

MSC:

20C20 Modular representations and characters
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16D90 Module categories in associative algebras

Citations:

Zbl 0699.00023