Low-dimensional cohomology of <italic>q</italic>-deformed Heisenberg-Virasoro algebra of Hom-type

doi:10.1007/s11464-010-0063-z

Front Math Chin

2010, Vol. 5

Issue (4) : 607-622 https://doi.org/10.1007/s11464-010-0063-z

RESEARCH ARTICLE

Low-dimensional cohomology of q-deformed Heisenberg-Virasoro algebra of Hom-type

Yongsheng CHENG^1,2(

), Hengyun YANG³

1. Institute of Contemporary Mathematics & School of Mathematics and Information Science, Henan University, Kaifeng 475004, China; 2. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China; 3. Department of Basic Sciences, Shanghai Maritime University, Shanghai 200135, China

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Abstract

Hom-Lie algebras were introduced by J. Hartwig, D. Larsson, and S. Silvestrov as a generalized Lie algebra. When studying the homology and cohomology theory of Hom-Lie algebras, the authors find that the lowdimensional cohomology theory of Hom-Lie algebras is not well studied because of the Hom-Jacobi identity. In this paper, the authors compute the first and second cohomology groups of the q-deformed Heisenberg-Virasoro algebra of Hom-type, which will be useful to build the low-dimensional cohomology theory of Hom-Lie algebras.

Keywords Hom-Lie algebra q-deformed Heisenberg-Virasoro algebra of Hom-type derivation cohomology group

Corresponding Author(s): CHENG Yongsheng,Email:yscheng@ustc.edu.cn

Issue Date: 05 December 2010

Cite this article:

Yongsheng CHENG,Hengyun YANG. Low-dimensional cohomology of q-deformed Heisenberg-Virasoro algebra of Hom-type[J]. Front Math Chin, 2010, 5(4): 607-622.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0063-z
https://academic.hep.com.cn/fmc/EN/Y2010/V5/I4/607

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