无性群上分级 PI 算法的最小品种

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-05-27 DOI:10.1112/blms.13064

Sebastiano Argenti, Onofrio Mario Di Vincenzo

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摘要

设 F $F$ 为特征为零的域，G $G$ 为有限无边群。本文将证明，当且仅当 G $G$ 分级 PI 算法的仿射变种是由上块三角形矩阵的分级代数 U T ( A 1 , ⋯ , A m ; γ ) $UT(A_1,\dots,A_m;\gamma)$ 生成时，它是最小的，其中 A 1 , ⋯ , A m $A_1,\dots,A_m$ 是有限维的 G $G$ 简单算法。

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Minimal varieties of graded PI-algebras over abelian groups

Let $F$ be a field of characteristic zero and $G$ a finite abelian group. In this paper, we prove that an affine variety of $G$ -graded PI-algebras is minimal if and only if it is generated by a graded algebra $U T (A_{1}, \dots, A_{m}; γ)$ of upper block triangular matrices where $A_{1}, \dots, A_{m}$ are finite-dimensional $G$ -simple algebras.