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...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.展开更多
文摘本文探讨了二维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.
