Abstract
We show that Brauer-Fitting correspondence as well as the notion of pseudoblocks of endomorphism algebras are both compatible with the external tensor product of modules and algebras.
Highlights
The tensor product of algebras and modules has been a subject for investigation by many authors in the past few decades
The concept of pseudo-blocks for endomorphism algebras was introduced in [8] where it was shown (Theorem2) that the distribution of the indecomposable summand of a module among the pseudo-blocks is compatible with the (Brauer) block distribution of the corresponding (under Brauer-Fitting correspondence) irreducible representations for the endomorphism algebra of that module
First we show that the Brauer-Fitting correspondence is compatible with the external tensoring of modules and algebras in the following sense
Summary
The tensor product of algebras and modules has been a subject for investigation by many authors in the past few decades. Külshammer [9] studied the tensor product of algebra and modules over an algebraically closed field. The concept of pseudo-blocks for endomorphism algebras was introduced in [8] where it was shown (Theorem2) that the distribution of the indecomposable summand of a module among the pseudo-blocks is compatible with the (Brauer) block distribution of the corresponding (under Brauer-Fitting correspondence (see section1)) irreducible representations for the endomorphism algebra of that module. In this paper we relate the Brauer-Fitting correspondence as well as the notion of pseudo-blocks to the external tensor product of modules and algebras.
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