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

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

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