41 citations · 252 across the 36 of their papers we have counts for
9 papers · 1 filter
Duality for graded Lie algebras
Andrey Lazarev, Rong Tang
A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology,…
Quasi-triangular, factorizable Leibniz bialgebras and relative Rota-Baxter operators
Chengming Bai, Guilai Liu, Yunhe Sheng +1
We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang-Baxter equation (CLYBE) whose skew-symmetric p…
Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation
Chengming Bai, Li Guo, Yunhe Sheng +1
The notions of a post-group and a pre-group are introduced as a unification and enrichment of several group structures appearing in diverse areas from numerical integration to the…
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…
Crossed homomorphisms and Cartier-Kostant-Milnor-Moore theorem for difference Hopf algebras
Li Guo, Yunnan Li, Yunhe Sheng +1
The celebrated Milnor-Moore theorem and the more general Cartier-Kostant-Milnor-Moore theorem establish close relationships of a connected and a pointed cocommutative Hopf algebra…
Deformations and homotopy theory of relative Rota-Baxter Lie algebras
Andrey Lazarev, Yunhe Sheng, Rong Tang
We determine the \emph{-algebra} that controls deformations of a relative Rota-Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling defor…
Homotopy relative Rota-Baxter Lie algebras, triangular -bialgebras and higher derived brackets
Andrey Lazarev, Yunhe Sheng, Rong Tang
We describe -algebras governing homotopy relative Rota-Baxter Lie algebras and triangular -bialgebras, and establish a map between them. Our formulas are based…
Homotopy Rota-Baxter operators, homotopy -operators and homotopy post-Lie algebras
Rong Tang, Chengming Bai, Li Guo +1
Rota-Baxter operators, -operators on Lie algebras and their interconnected pre-Lie and post-Lie algebras are important algebraic structures with applications in mathem…
Deformations and their controlling cohomologies of -operators
Rong Tang, Chengming Bai, Li Guo +1
-operators are important in broad areas in mathematics and physics, such as integrable systems, the classical Yang-Baxter equation, pre-Lie algebras and splitting of o…