Korean J. Math. Vol. 29 No. 2 (2021) pp.271-291
DOI: https://doi.org/10.11568/kjm.2021.29.2.271

Cohomology and deformations of Hom-Lie-Yamaguti color algebras

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A. Nourou Issa


Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The $(2,3)$-cocycles of a given Hom-Lie-Yamaguti color algebra $T$ are shown to be very useful in a study of its deformations. In particular, it is shown that any $(2,3)$-cocycle of $T$ gives rise to a Hom-Lie-Yamaguti color structure on $T \oplus V$, where $V$ is a $T$-module, and that a one-parameter infinitesimal deformation of $T$ is equivalent to that a $(2,3)$-cocycle of $T$ (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

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