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On the central exponent of superalgebras with superinvolution

Part of: Rings and algebras with additional structure Rings with polynomial identity Representation theory of groups

Published online by Cambridge University Press:  22 September 2025

Ginevra Giordani ,
Antonio Ioppolo Open the ORCID record for Antonio Ioppolo [Opens in a new window] ,
Antônio dos Santos  and
Ana Vieira
Ginevra Giordani
Affiliation:
Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila , Via Vetoio 1, 67100 L’Aquila, Italy e-mail: ginevra.giordani@graduate.univaq.it antonio.ioppolo@univaq.it
Antonio Ioppolo
Affiliation:
Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila , Via Vetoio 1, 67100 L’Aquila, Italy e-mail: ginevra.giordani@graduate.univaq.it antonio.ioppolo@univaq.it
Antônio dos Santos
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais , Avenida Antonio Carlos 6627, Belo Horizonte 31123-970, Brazil e-mail: aapds1510@gmail.com
Ana Vieira*
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais , Avenida Antonio Carlos 6627, Belo Horizonte 31123-970, Brazil e-mail: aapds1510@gmail.com
*
e-mail: anacris@ufmg.br
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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.

Keywords

Central polynomialidentitysuperinvolutionexponentgrowth

MSC classification

Primary: 16R10: $T$-ideals, identities, varieties of rings and algebras 16R50: Other kinds of identities (generalized polynomial, rational, involution)
Secondary: 16W10: Rings with involution; Lie, Jordan and other nonassociative structures 16W50: Graded rings and modules 20C30: Representations of finite symmetric groups

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

G.G. and A.I. were partially supported by INdAM - GNSAGA. A.A.P.d. was partially supported by CAPES. A.C.V. was partially supported by FAPEMIG and by CNPq.

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