李代数W(2,2)上的Hom-李代数结构
The Hom-Lie Structure on the Lie Algebra W (2, 2)
李代数W(2,2)是一类重要的无限维李代数,它是在研究权为2的向量生成的顶点算子代数的过程当中提出来的.Hom-李代数是指同时具备代数结构和李代数结构的一类代数,并且乘法与李代数乘法运算满足Leibniz法则.本文确定了李代数W(2,2)上的Hom-李代数结构.主要结论是李代数W(2,2)上没有非平凡的Hom-李代数结构.本文的研究结果对于W(2,2)代数的进一步研究有一定的帮助作用.
The Lie algebra W (2, 2) is one kind of infinite-dimensional Lie algebras, which plays a key role in classification of vertex operator algebras generated by weight 2 vectors. Hom-Lie algebras are algebras with an algebra structure and a Lie algebra structure, both of which satisfy the Leibniz rule. This paper mainly determine all Hom-Lie structures on the Lie algebra W (2, 2). It is the main result that all Hom-Lie algebra structures are trivial on the Lie algebra W (2, 2), which will be helpful to the further researches on the Lie algebra W (2, 2).
李代数W(2 / 2) / Hom-李代数 / 自同态 {{custom_keyword}} /
Lie algebra W (2, 2) / Hom-Lie algebra / endomorphism {{custom_keyword}} /
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国家自然科学基金项目(11971315,11871249)
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