二维ω-反左对称代数的分类
The Classification of 2-Dimensional ω-Anti-Left Symmetric Algebras
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。
Abstract: 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.
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