二维ω-反左对称代数的分类  

The Classification of 2-Dimensional ω-Anti-Left Symmetric Algebras

作　　者：王秋艳 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《理论数学》2024年第11期246-258,共13页Pure Mathematics

摘　　要：本文探讨了二维ω-反左对称代数的基本性质及其低维分类。首先,引入ω-反左对称代数的定义,研究其与ω-李代数的代数结构和表示之间的关系。然后通过ω-反左对称代数与ω-李代数的关系,研究二维ω-反左对称代数的代数运算,给出在二维的情况下实数域和复数域上ω-反左对称代数的完全分类。This paper explores the fundamental properties and classification of two-dimensional ω-anti-pre algebras. First, we introduce the definition of ω-anti-pre algebras and study the relationship between ω-anti-pre algebras and ω-Lie algebras in the algebraic structure and representation. Then through the relationship between ω-anti-pre algebras and ω-Lie algebras, we study the algebraic operations of two-dimensional ω-anti-pre algebras and provide a complete classification of ω-anti-pre algebras over the real and complex fields in the two-dimensional case.

关 键 词：ω-反左对称代数 ω-李代数 同构 

分 类 号：O15[理学—数学]