A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916779479007232 |
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| author | Fuchs, Jürgen Grøsfjeld, Tobias |
| author_facet | Fuchs, Jürgen Grøsfjeld, Tobias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras Fuchs, Jürgen Grøsfjeld, Tobias Quantum Algebra Category Theory 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. |
| title | A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras |
| topic | Quantum Algebra Category Theory |
| url | https://arxiv.org/abs/2403.10366 |