On existence of PI-exponent of algebras with involution

Dušan Repovš (Author), Mikhail Zaicev (Author)

Abstract

We study polynomial identities of algebras with involution of nonassociative algebras over a field of characteristic zero. We prove that the growth of the sequence of *-codimensions of a finite-dimensional algebra is exponentially bounded. We construct a series of finite-dimensional algebras with fractional -PI-exponent. We also construct a family of infinite-dimensional algebras ▫$C_\alpha* $▫ such that ▫$\exp^\ast (C_\alpha)$▫ does not exist.

Keywords

polynomial identity;nonassociative algebra;involution;exponential growth;exponentially bounded *-codimension;fractional *-PI-exponent;Amitsur's conjecture;numerical invariant;

Data

Language:	English
Year of publishing:	2023
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	512.554.3
COBISS:	126194179
ISSN:	0021-8693
Views:	150
Downloads:	56
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 5-19
Issue:	ǂVol. ǂ614
Chronology:	Jan. 2023
DOI:	10.1016/j.jalgebra.2022.09.013
ID:	16812125