Graded group actions and generalized $H$-actions compatible with gradings
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916746920722432 |
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| author | Gordienko, A. S. |
| author_facet | Gordienko, A. S. |
| contents | We introduce the notion of a graded group action on a graded algebra or, which is the same, a group action by graded pseudoautomorphisms. An algebra with such an action is a natural generalization of an algebra with a super- or a pseudoinvolution. We study groups of graded pseudoautomorphisms, show that the Jacobson radical of a group graded finite dimensional associative algebra $A$ over a field of characteristic $0$ is stable under graded pseudoautomorphisms, prove the invariant version of the Wedderburn-Artin Theorem and the analog of Amitsur's conjecture for the codimension growth of graded polynomial $G$-identities in such algebras $A$ with a graded action of a group $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00874 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graded group actions and generalized $H$-actions compatible with gradings Gordienko, A. S. Rings and Algebras Primary 16W22, Secondary 16R10, 16R50, 16T05, 16W20, 16W25, 16W50, 16W55, 17A01 We introduce the notion of a graded group action on a graded algebra or, which is the same, a group action by graded pseudoautomorphisms. An algebra with such an action is a natural generalization of an algebra with a super- or a pseudoinvolution. We study groups of graded pseudoautomorphisms, show that the Jacobson radical of a group graded finite dimensional associative algebra $A$ over a field of characteristic $0$ is stable under graded pseudoautomorphisms, prove the invariant version of the Wedderburn-Artin Theorem and the analog of Amitsur's conjecture for the codimension growth of graded polynomial $G$-identities in such algebras $A$ with a graded action of a group $G$. |
| title | Graded group actions and generalized $H$-actions compatible with gradings |
| topic | Rings and Algebras Primary 16W22, Secondary 16R10, 16R50, 16T05, 16W20, 16W25, 16W50, 16W55, 17A01 |
| url | https://arxiv.org/abs/2309.00874 |