左对称代数上的自反逆
Reflexive g-Inverse on Left-Symmetric Algebras
摘要: 本文给出了自反逆在左对称代数上的定义，证明了自反逆在低维左对称代数的存在性。 在低维左 对称代数分类中，发现了三类可延拓至n维的非结合左对称代数，井证明了自反逆在这三类n维代 数上的存在性。
Abstract: In this paper, we give the definition of reflexive g-inverse on left-symmetric alge- bras. Based on the classifications of low-dimensional LSAs, we prove the existence of reflexive g-inverses on low-dimensional cases. Then, we extend three classes of three- dimensional left-symmetric algebras which are non-associative to n-dimensional cases, and prove the existence of reflexive g-inverse in n-dimensional cases.
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