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• W3204693248 startingPage "106920" @default.
• W3204693248 abstract "Let A be a finitely generated superalgebra with pseudoinvolution ⁎ over an algebraically closed field F of characteristic zero. In this paper we develop a theory of polynomial identities for this kind of algebras. In particular, we shall consider three sequences that can be attached to Id⁎(A), the T2⁎-ideal of identities of A: the sequence of ⁎-codimensions cn⁎(A), the sequence of ⁎-cocharacter χ〈n〉⁎(A) and the ⁎-colength sequence ln⁎(A). Our purpose is threefold. First we shall prove that the ⁎-codimension sequence is eventually non-decreasing, i.e., cn⁎(A)≤cn+1⁎(A), for n large enough. Secondly, we study superalgebras with pseudoinvolution having the multiplicities of their ⁎-cocharacter bounded by a constant. Among them, we characterize the ones with multiplicities bounded by 1. Finally, we classify superalgebras with pseudoinvolution A such that ln⁎(A) is bounded by 3. In the last section we relate the ⁎-colengths with the polynomial growth of the ⁎-codimensions: we show that ln⁎(A) is bounded by a constant if and only if cn⁎(A) grows at most polynomially." @default.
• W3204693248 created "2021-10-11" @default.
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• W3204693248 date "2022-05-01" @default.
• W3204693248 modified "2023-10-16" @default.
• W3204693248 title "Varieties of algebras with pseudoinvolution: Codimensions, cocharacters and colengths" @default.
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• W3204693248 doi "https://doi.org/10.1016/j.jpaa.2021.106920" @default.
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