6533b838fe1ef96bd12a48a7

RESEARCH PRODUCT

Varieties of algebras with pseudoinvolution and polynomial growth

Antonio IoppoloFabrizio Martino

subject

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: 16W10Mathematics

description

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 describe the algebras with pseudoinvolution whose (Formula presented.) -codimensions are bounded by a linear function.

yearjournalcountryeditionlanguage
2017-10-28Linear and Multilinear Algebra
https://doi.org/10.1080/03081087.2017.1394257