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arXiv · 2403.10366

A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras

Jürgen Fuchs·Tobias Grøsfjeld
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Abstract

We consider algebras and Frobenius algebras, internal to a monoidal category, that are graded over a finite abelian group. For the case that A is a twisted group algebra in a linear abelian monoidal category we obtain a graded generalization of the Schur Lemma for the category of induced A-modules. We further show that if the monoidal category is braided and A is commutative up to a bicharacter of the grading group, then the category of induced A-modules can be endowed with a graded-monoidal structure that is twisted by the bicharacter. In the particular case that the grading group is Z/2Z, these findings reproduce known results about superalgebras and super-monoidal structures.

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Jürgen Fuchs, Tobias Grøsfjeld. 2024-03-15. A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras. https://doi.org/10.1080/00927872.2025.2472241

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