290 citations · 1.2k across the 89 of their papers we have counts for
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A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras
Yunhe Sheng
In this paper, we review deformation, cohomology and homotopy theories of relative Rota-Baxter Lie algebras, which have attracted quite much interest recently. Using Voronov's high…
Cohomologies of difference Lie groups and van Est theorem
Jun Jiang, Yunnan Li, Yunhe Sheng
A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce…
Deformations and homotopy of Rota-Baxter operators and -operators on Lie algebras
Rong Tang, Chengming Bai, Li Guo +1
This article gives a brief introduction to some recent work on deformation and homotopy theories of Rota-Baxter operators and more generally -operators on Lie algebras…
Deformations, cohomologies and abelian extensions of compatible -Lie algebras
Shuai Hou, Yunhe Sheng
In this paper, first we give the notion of a compatible -Lie algebra and construct a bidifferential graded Lie algebra whose Maurer-Cartan elements are compatible -Lie algebr…
Deformations of modified -matrices and cohomologies of related algebraic structures
Jun Jiang, Yunhe Sheng
Modified -matrices are solutions of the modified classical Yang-Baxter equation, introduced by Semenov-Tian-Shansky, and play important roles in mathematical physics. In this pa…
Coherent categorical structures for Lie bialgebras, Manin triples, classical -matrices and pre-Lie algebras
Chengming Bai, Li Guo, Yunhe Sheng
The broadly applied notions of Lie bialgebras, Manin triples, classical -matrices and -operators of Lie algebras owe their importance to the close relationship amon…
Nonabelian embedding tensors
Rong Tang, Yunhe Sheng
In this paper, first we introduce the notion of a nonabelian embedding tensor, which is a nonabelian generalization of an embedding tensor. Then we introduce the notion of a Leibni…
-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on -Lie algebras
Shuai Hou, Yunhe Sheng, Yanqiu Zhou
In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on -Lie algebras and -post-Lie algebras. A 3-post-Lie algebra consists of a…
Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation
Yunnan Li, Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf al…
Deformations, cohomologies and integrations of relative difference Lie algebras
Jun Jiang, Yunhe Sheng
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differen…