Minimal *-varieties and minimal supervarieties of polynomial growth

JOURNAL OF ALGEBRA

卷:552

Article

Gouveia, Tatiana Aparecida^1,2  dos Santos, Rafael Bezerra²  Vieira, Ana Cristina² 

[1] Univ Fed Juiz de For, Inst Ciencias Exatas, Dept Matemat, Rua Jose Lourenco Kelmer S-N, Martelos, Juiz De Fora, Brazil

[2] Univ Fed Minas Gerais, Inst Ciencias Exatas, Dept Matemat, Ave Antonio Carlos 6627, Belo Horizonte, MG, Brazil

关键词: Polynomial identity;    Minimal variety;    Polynomial growth;    Algebra with involution;    Superalgebra;   

DOI  :  10.1016/j.jalgebra.2020.02.009

来源: Elsevier

【 摘 要 】

By a phi-variety nu, we mean a supervariety or a *-variety generated by an associative algebra over a field F of characteristic zero. In this case, we consider its sequence of phi-codimensions c(n)(phi)(nu) and say that nu is minimal of polynomial growth n(k) if c(n)(phi)(nu) grows like n(k), but any proper phi-subvariety grows like n(t) with t < k. In this paper, we deal with minimal phi-varieties generated by unitary algebras and prove that for k <= 2 there is only a finite number of them. We also explicit a list of finite dimensional algebras generating such minimal phi-varieties. For k >= 3, we show that the number of minimal phi-varieties can be infinity and we classify all minimal phi-varieties of polynomial growth n(k) by giving a recipe for the construction of their T-phi-ideals. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free