李代数W(2,2)上的Hom-李代数结构

陈海波, 赖丹丹, 刘东

数学学报 ›› 2020, Vol. 63 ›› Issue (4) : 403-408.

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PDF(371 KB)
数学学报 ›› 2020, Vol. 63 ›› Issue (4) : 403-408. DOI: 10.12386/A2020sxxb0034
论文

李代数W(2,2)上的Hom-李代数结构

    陈海波1, 赖丹丹2, 刘东2
作者信息 +

The Hom-Lie Structure on the Lie Algebra W (2, 2)

    Hai Bo CHEN1, Dan Dan LAI2, Dong LIU2
Author information +
文章历史 +

摘要

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.

Abstract

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).

关键词

李代数W(2 / 2) / Hom-李代数 / 自同态

Key words

Lie algebra W (2, 2) / Hom-Lie algebra / endomorphism

引用本文

导出引用
陈海波, 赖丹丹, 刘东. 李代数W(2,2)上的Hom-李代数结构. 数学学报, 2020, 63(4): 403-408 https://doi.org/10.12386/A2020sxxb0034
Hai Bo CHEN, Dan Dan LAI, Dong LIU. The Hom-Lie Structure on the Lie Algebra W (2, 2). Acta Mathematica Sinica, Chinese Series, 2020, 63(4): 403-408 https://doi.org/10.12386/A2020sxxb0034

参考文献

[1] Hartwig J. T., Larsson D., Silvestrov S. D., Deformations of Lie algebras using σ-derivations, Journal of Algebra, 2006, 295:314-361.
[2] Hu N. H., q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebra Colloq., 1999, 6(1):51-70.
[3] Jin Q. Q., Li X. C., Hom-structures on semi-simple Lie algebras, Journal of Algebra, 2008, 319(4):1398-1408.
[4] Li X. C., Hom-Lie algebra structure on the Virasoro algebra, Journal of Zhoukou Normal University, 2009, 26(5):3-4.
[5] Li Y. N., Gao S. L., Liu D., Poisson structure on the Lie algebra W (2, 2) (in Chinese), Chinese Ann. Math. Ser. A, 2016, 37(3):267-272
[6] Liu D., Gao S. L., Zhu L. S., Classification of irreducible weight modules over the W -algebra W (2, 2), Journal of Mathematical Physics, 2008, 49, 113503, 6 pp.
[7] Makhlouf A., Zusmanovich P., Hom-Lie structures on Kac-Moody algebras, Journal of Algebra, 2018, 515:278-297.
[8] Zhang W., Dong C. Y., W -algebra W (2, 2) and the vertex operator algebra L(1/2, 0) ⊗ L(1/2, 0), Commun. Math. Phys., 2009, 285(3):991-1004.
[9] Zhao K. M., Automorphisms and homomorphisms of the Virasoro algebra (in Chinese), J. Systems Sci. Math. Sci., 1992, 12(1):1-4.
[10] Zhao X. X., Gao S. L., Liu D., Poisson structure on the twisted Heisenberg-Virasoro algebra, Acta Math. Sinica Chin. Ser., 2016, 59(6):775-782.

基金

国家自然科学基金项目(11971315,11871249)

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