*-superalgebras and exponential growth

• Autor(a) principal: Rafael Bezerra Dos Santos
• Data de Publicação: 2017
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: https://doi.org/10.1016/j.jalgebra.2016.10.029; http://hdl.handle.net/1843/37243; https://orcid.org/0000-0002-9056-5624
• topic: Polynomial identity; Graded involution; Exponential growth; ⁎-Graded exponent; Superálgebras; Álgebras associativas

In this paper, we study the exponential growth of ∗-graded identities of a finite dimensional ∗-superalgebra Aover a field Fof characteristic zero. If a ∗-superalgebra Asatisfies a non-trivial identity, then the sequence {cgrin(A)}n≥1of ∗-graded codimensions of Ais exponentially bounded and so we study the ∗-graded exponent expgri(A) := limn→∞n√cgrin(A)of A. We show that expgri(A) =dimF(A)if and only if Ais a simple ∗-superalgebra and Fis the symmetric even center of A. Also, we characterize the finite dimensional ∗-superalgebras such that expgri(A) ≤1by the exclusion of four ∗-superalgebras from vargri(A)and construct eleven ∗-superalgebras Ei, i =1, ..., 11, with the following property: expgri(A) >2if and only if Ei∈vargri(A), for some i ∈{1, ..., 11}. As a consequence, we characterize the finite dimensional ∗-superalgebras Asuch that expgri(A) =2