Twisted Rota-Baxter families on Lie-Yamaguti algebras and NS-Lie-Yamaguti family algebras

2025/09/30 by Teng, Wen
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2509.25619

Abstract

In this paper, we first introduce twisted Rota-Baxter families on Lie-Yamaguti algebras indexed by a commutative semigroup Ω. 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 Ω-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.

Citations

• Twisting O-operators by (2,3)-Cocycle of Hom-Lie-Yamaguti Algebras with Representations
• Twisted Rota-Baxter family operators on Hom-associative algebras
• Deformation Cohomology of Lie-Yamaguti algebras and Free Lie-Yamaguti algebras
• Twisted Rota-Baxter families and NS-family algebras
• Relative Rota-Baxter operators and symplectic structures on Lie-Yamaguti algebras
• Free pre-Lie family algebras
• Generalized dendrifom algebras and typed binary trees
• Deformations and extensions of Lie–Yamaguti algebras
• Symmetric matrices, orthogonal Lie algebras, and Lie-Yamaguti algebras
• Hopf algebraic Renormalization of Kreimer's toy model
• Irreducible Lie-Yamaguti algebras of Generic Type
• Irreducible Lie–Yamaguti algebras of generic type
• Irreducible Lie-Yamaguti algebras
• Irreducible Lie–Yamaguti algebras
• Poisson geometry with a 3-form background
• Leibniz Algebras, Courant Algebroids, and Multiplications on Reductive Homogeneous Spaces
• Invariant Affine Connections on Homogeneous Spaces

Related

• Modified Rota-Baxter Lie-Yamaguti algebras
• Twisted Rota-Baxter families and NS-family algebras
• Cohomology and deformations of Relative Rota-Baxter operators on Lie-Yamaguti algebras
• Post Lie-Yamaguti algebras, relative Rota-Baxter operators of nonzero weights, and their deformations
• Twisted Rota-Baxter family operators on Hom-associative algebras