On the central exponent of superalgebras with superinvolution
Abstract The growth of central polynomials for matrix algebras over a field of characteristic zero was first studied by Regev in $2016$ . This problem can be generalized by analyzing the behavior of the dimension $c_n^z(A)$ of the space of multilinear polynomials of degree n modulo the central polynomials of an algebra A . In $2018$ , Giambruno and Zaicev established the existence of the limit $\lim \limits _{n \to \infty }\sqrt [n]{c_n^{z}(A)}.$ In this article, we extend this framework to superalgebras equipped with a superinvolution, proving both the existence and the finiteness of the corresponding limit.
Authors
- Antonio Ioppolo (ORCID: https://orcid.org/0000-0003-4774-5483)
- Ginevra Giordani (ORCID: https://orcid.org/0009-0000-6218-4261)
- Ana Cristina Vieira (ORCID: https://orcid.org/0000-0002-8891-3319)
- A. A. P. Dos Santos
Institutions
- Universidade Federal de Minas Gerais (BR)
- University of L'Aquila (IT)
Publication Details
- Journal
- Canadian Mathematical Bulletin
- Published
- 2025-09-22
- DOI
- https://doi.org/10.4153/s0008439525101276
- Primary Topic
- Advanced Topics in Algebra
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação de Amparo à Pesquisa do Estado de Minas Gerais
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni