Let $F$ be a field of characteristic zero and $p$ a prime. In the present paper it is proved that a variety of $Z_p$-graded associative PI $F$-algebras of finite basic rank is minimal of fixed $Z_p$-exponent $d$ if, and only if, it is generated by an upper block triangular matrix algebra $UT_{Z_p}(A_1,ldots, A_m)$ equipped with a suitable elementary $Z_p$-grading, whose diagonal blocks are isomorphic to $Z_p$-graded simple algebras $A_1,ldots,A_m$ satisfying $dim_F (A_1 opluscdotsoplus A_m)=d$.
A characterization of minimal varieties of Z_p-graded PI algebras / Di Vincenzo, Onofrio Mario; da Silva, Viviane Ribeiro Tomaz; Spinelli, Ernesto. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 539:(2019), pp. 397-418. [10.1016/j.jalgebra.2019.08.018]
A characterization of minimal varieties of Z_p-graded PI algebras
Di Vincenzo, Onofrio Mario;da Silva, Viviane Ribeiro Tomaz;Spinelli, Ernesto
2019
Abstract
Let $F$ be a field of characteristic zero and $p$ a prime. In the present paper it is proved that a variety of $Z_p$-graded associative PI $F$-algebras of finite basic rank is minimal of fixed $Z_p$-exponent $d$ if, and only if, it is generated by an upper block triangular matrix algebra $UT_{Z_p}(A_1,ldots, A_m)$ equipped with a suitable elementary $Z_p$-grading, whose diagonal blocks are isomorphic to $Z_p$-graded simple algebras $A_1,ldots,A_m$ satisfying $dim_F (A_1 opluscdotsoplus A_m)=d$.File | Dimensione | Formato | |
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