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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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참고문헌 (31)
참고문헌 신청
K. Abdaoui / 2015 / Constructions and cohomology of Hom-Lie color algebras / Comm. Algebra 43(11):4581~4612
F. Ammar / 2020 / Quadratic color Hom-Lie algebras / As-sociative and Nonassociative Algebras and Applications, Springer Proceedings in Mathematics and Statistics book series 311:287~312
F. Ammar / 2011 / Cohomology and deformations of Hom-algebras / J. Lie Theory 21(4):813~836
F. Ammar / 2013 / Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra / Czechoslovak Math. J 63(3):721~761
A. S. Dzhumadil’daev / 2000 / Cohomology of colour Leibniz algebras: pre-simplicial approach / Lie Theory and its Applications in Physics III. Proceedings of the Third International Workshop :124~136
F. Ammar / 2020 / Quadratic color Hom-Lie algebras / As-sociative and Nonassociative Algebras and Applications, Springer Proceedings in Mathematics and Statistics book series 311:287~312
F. Ammar / 2011 / Cohomology and deformations of Hom-algebras / J. Lie Theory 21(4):813~836
F. Ammar / 2013 / Cohomology of Hom-Lie superalgebras and q-deformed Witt superalgebra / Czechoslovak Math. J 63(3):721~761
A. S. Dzhumadil’daev / 2000 / Cohomology of colour Leibniz algebras: pre-simplicial approach / Lie Theory and its Applications in Physics III. Proceedings of the Third International Workshop :124~136
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