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Derivations and deformations of Lie-Yamaguti color algebras. (English) Zbl 1499.17008

Summary: In this paper, we introduce the representation and cohomology theory of Lie-Yamaguti color algebras. Furthermore, we introduce the notions of generalized derivations of Lie-Yamaguti color algebras and present some properties. Finally, we study linear deformations of Lie-Yamaguti color algebras, and introduce the notion of a Nijenhuis operator on a Lie-Yamaguti color algebra, which can generate a trivial deformation.

MSC:

17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
17A40 Ternary compositions
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B56 Cohomology of Lie (super)algebras
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