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Minimal varieties of PI-superalgebras with graded involution

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Abstract

In the present paper it is proved that a variety of associative PI-superalgebras with graded involution of finite basic rank over a field of characteristic zero is minimal of fixed *-graded exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra equipped with a suitable elementary ℤ2-grading and graded involution.

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Authors and Affiliations

  1. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Via dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Onofrio Mario Di Vincenzo

  2. Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 30161-970, Belo Horizonte, Brazil

    Viviane Ribeiro Tomaz da Silva

  3. Dipartimento di Matematica “G. Castelnuovo”, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185, Roma, Italy

    Ernesto Spinelli

Authors
  1. Onofrio Mario Di Vincenzo
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  2. Viviane Ribeiro Tomaz da Silva
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  3. Ernesto Spinelli
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Corresponding author

Correspondence to Onofrio Mario Di Vincenzo.

Additional information

The authors thank the support of RIL of Università della Basilicata, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) — grant 306534/2016-9, Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) — grant APQ-01149-18 and Progetti di Ricerca d’Ateneo of Università di Roma “La Sapienza”.

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Di Vincenzo, O.M., da Silva, V.R.T. & Spinelli, E. Minimal varieties of PI-superalgebras with graded involution. Isr. J. Math. 241, 869–909 (2021). https://doi.org/10.1007/s11856-021-2119-z

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  • DOI: https://doi.org/10.1007/s11856-021-2119-z

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