6533b874fe1ef96bd12d62ee

RESEARCH PRODUCT

Varieties of Algebras with Superinvolution of Almost Polynomial Growth

Antonio IoppoloDaniela La MattinaAntonio Giambruno

subject

SequencePolynomialSuperinvolutionGeneral Mathematics010102 general mathematicsGrowth; Polynomial identity; SuperinvolutionZero (complex analysis)Field (mathematics)010103 numerical & computational mathematicsGrowthPolynomial identity01 natural sciencesExponential functionCombinatoricsSettore MAT/02 - AlgebraBounded functionAssociative algebraMathematics (all)0101 mathematicsVariety (universal algebra)Mathematics

description

Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let $c_{n}^{\ast }(A)$ be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.

yearjournalcountryeditionlanguage
2015-12-28
10.1007/s10468-015-9590-3http://hdl.handle.net/10447/199187