Twisted Rota-Baxter families on Lie-Yamaguti algebras and NS-Lie-Yamaguti family algebras
Abstract
In this paper, we first introduce twisted Rota-Baxter families on Lie-Yamaguti algebras indexed by a commutative semigroup . Then, we study NS-Lie-Yamaguti family algebras as the underlying structures of twisted Rota-Baxter families. Finally, we investigate the cohomology of a twisted Rota-Baxter family. This cohomology can also be seen as the cohomology of a certain -Lie-Yamaguti algebras with coefficients in an appropriate representation. As applications, we consider the deformations of twisted Rota-Baxter families from the cohomological points of view.
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