Search results for "pseudoinvolution"

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Varieties of algebras with pseudoinvolution and polynomial growth

2017

Let A be an associative algebra with pseudoinvolution (Formula presented.) over an algebraically closed field of characteristic zero and let (Formula presented.) be its sequence of (Formula presented.) -codimensions. We shall prove that such a sequence is polynomially bounded if and only if the variety generated by A does not contain five explicitly described algebras with pseudoinvolution. As a consequence, we shall classify the varieties of algebras with pseudoinvolution of almost polynomial growth, i.e. varieties of exponential growth such that any proper subvariety has polynomial growth and, along the way, we shall give also the classification of their subvarieties. Finally, we shall de…

16R50; 16W50; growth; Polynomial identity; Primary: 16R10; pseudoinvolution; Secondary: 16W10Linear function (calculus)PolynomialPure mathematicspseudoinvolutionAlgebra and Number TheorySubvariety16R50growth010102 general mathematicsPolynomial identity pseudo involution codimension growthZero (complex analysis)010103 numerical & computational mathematicsPolynomial identity01 natural sciencesPrimary: 16R10Settore MAT/02 - AlgebraBounded functionAssociative algebra0101 mathematicsAlgebraically closed fieldVariety (universal algebra)16W50Secondary: 16W10MathematicsLinear and Multilinear Algebra
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Varieties of algebras with pseudoinvolution: Codimensions, cocharacters and colengths

2022

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 T 2 ⁎ -ideal of identities of A: the sequence of ⁎-codimensions c n ⁎ ( A ) , the sequence of ⁎-cocharacter χ 〈 n 〉 ⁎ ( A ) and the ⁎-colength sequence l n ⁎ ( A ) . Our purpose is threefold. First we shall prove that the ⁎-codimension sequence is eventually non-decreasing, i.e., c n ⁎ ( A ) ≤ c n + 1 ⁎ ( A ) , for n large enough. Secondly, we study superalgebras with pseudoinvoluti…

ColengthsPolynomialSequencePure mathematicsMultiplicitiesAlgebra and Number TheoryMathematics::Commutative AlgebraPseudoinvolutionsZero (complex analysis)Cocharacters; Colengths; Multiplicities; Polynomial identities; PseudoinvolutionsCocharactersSuperalgebraPolynomial identitiesSettore MAT/02 - AlgebraSection (category theory)Bounded functionIdeal (ring theory)Algebraically closed fieldMathematics
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