Periodic Algebras Generated by Groups

• 作者: B.A. Omirov S. Albeverio U.A. Rozikov
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: c代数 周期 莱布尼茨 C函数 幂零性 新西兰 性质 乘法
• 年，卷（期）: 2015,（4）
• 页码范围: 541-554
• 页数: 14页
• 分类号: O177.5
• 语种: 中文

摘要

We consider algebras with basis numerated by elements of a group G. We fix a function f from G * G to a ground field and give a multiplication of the algebra which depends on f. We study the basic properties of such algebras. In particular, we find a condition on f under which the corresponding algebra is a Leibniz algebra. Moreover, for a given subgroup G of G we define a G-periodic algebra, which corresponds to a G-periodic function f, we establish a criterion for the right nilpotency of a G-periodic algebra. In addition, for (7 = Z we describe all 2Z- and 3Z-periodic algebras. Some properties of nZ-periodic algebras are obtained.