On existence of PI-exponent of algebras with involution

Dušan Repovš (Avtor), Mikhail Zaicev (Avtor)

Povzetek

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.

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2023
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	512.554.3
COBISS:	126194179
ISSN:	0021-8693
Št. ogledov:	150
Št. prenosov:	56
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 5-19
Zvezek:	ǂVol. ǂ614
Čas izdaje:	Jan. 2023
DOI:	10.1016/j.jalgebra.2022.09.013
ID:	16812125