On existence of PI-exponent of algebras with involution

Repovš, Dušan (author), Zaicev, Mikhail V. (author)

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.

• Language: English
• Keywords: polynomial identity, nonassociative algebra, involution, exponential growth, exponentially bounded *-codimension, fractional *-PI-exponent, Amitsur's conjecture, numerical invariant
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 5-19
• Numbering: Vol. 614
• PID: 20.500.12556/RUL-142109
• UDC: 512.554.3
• ISSN on article: 0021-8693
• DOI: 10.1016/j.jalgebra.2022.09.013
• COBISS.SI-ID: 126194179
• Publication date in RUL: 20.10.2022

Record is a part of a journal

• Title: Journal of algebra
• Shortened title: J. algebra
• Publisher: Elsevier
• ISSN: 0021-8693
• COBISS.SI-ID: 1310986

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.