Abstract
Classifications of varieties of algebras of almost polynomial growth were considered by several authors in different contexts. An algebra graded by a group G and endowed with a graded involution ∗ is called a (G,∗)-algebra. In this paper, we study (G,∗)-algebras when G is a finite abelian group and we classify all varieties generated by finite dimensional (G,∗)-algebras of almost polynomial growth. Along the way, we characterize the finite dimensional simple (G,∗)-algebras and as a consequence, we classify the finite dimensional simple (Cp,∗)-algebras, for an odd prime p, over any algebraically closed field of characteristic zero.
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A.C. Vieira was partially supported by CNPq and FAPEMIG. The authors have no conflicts of interest to declare that are relevant to the content of this article. Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
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Presented by: Michel Van den Bergh
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Oliveira, L.M.C., dos Santos, R.B. & Vieira, A.C. Varieties of Group Graded Algebras with Graded Involution of Almost Polynomial Growth. Algebr Represent Theor 26, 663–677 (2023). https://doi.org/10.1007/s10468-021-10107-0
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DOI: https://doi.org/10.1007/s10468-021-10107-0