5 citations · 7 across the 12 of their papers we have counts for
14 papers
Cohomology theory of Novikov algebras and applications
Pavel Kolesnikov, Yue Li, Yunhe Sheng +1
In this paper, first we give a new characterization of the cohomology of pre-Lie algebras using the Chevalley-Eilenberg cohomology associated to a morphism from the operad of Lie a…
Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration
Adrien Busnot Laurent, Yunnan Li, Yunhe Sheng
In this paper, we introduce the notion of post-Hopf algebroids, generalizing the pre-Hopf algebroids introduced in [Bronasco, Laurent, 2025] in the study of exotic aromatic S-serie…
Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures
Yvain Bruned, Yunhe Sheng, Rong Tang
In this paper, we study post-Lie deformations of a pre-Lie algebra, namely deforming a pre-Lie algebra into a post-Lie algebra. We construct the differential graded Lie algebra tha…
Homotopy theory of post-Lie algebras
Andrey Lazarev, Yunhe Sheng, Rong Tang
In this paper, we study the homotopy theory of post-Lie algebras. Guided by Koszul duality theory, we consider the graded Lie algebra of coderivations of the cofree conilpotent gra…
Cohomology of Lie coalgebras
Joseph Chuang, Andrey Lazarev, Yunhe Sheng +1
A Koszul duality-type correspondence between coderived categories of conilpotent differential graded Lie coalgebras and their Chevalley-Eilenberg differential graded algebras is es…
On the integration of relative Rota-Baxter Lie algebras
Jun Jiang, Yunhe Sheng, Chenchang Zhu
In this paper, we give the necessary and sufficient conditions of the integrability of relative Rota-Baxter Lie algebras via double Lie groups, matched pairs of Lie groups and fact…
Post-groupoids and quiver-theoretical solutions of the Yang-Baxter equation
Yunhe Sheng, Rong Tang, Chenchang Zhu
The notion of post-groups was introduced by Bai, Guo and the first two authors recently, which are the global objects corresponding to post-Lie algebras, equivalent to skew-left br…
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…
Stability and rigidity of 3-Lie algebra morphisms
Jun Jiang, Yunhe Sheng, Geyi Sun
In this paper, first we use the higher derived brackets to construct an -algebra, whose Maurer-Cartan elements are -Lie algebra morphisms. Using the differential in th…
Deformation maps of quasi-twilled Lie algebras
Jun Jiang, Yunhe Sheng, Rong Tang
In this paper, we provide a unified approach to study the cohomology theories and deformation theories of various types of operators in the category of Lie algebras, including modi…
Formal integration of complete Rota-Baxter Lie algebras
Maxim Goncharov, Pavel Kolesnikov, Yunhe Sheng +1
In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases. Then we establish the formal integration theory for complet…
Cohomology and Homotopy of Lie triple systems
Haobo Xia, Yunhe Sheng, Rong Tang
In this paper, first we give the controlling algebra of Lie triple systems. In particular, the cohomology of Lie triple systems can be characterized by the controlling algebra. The…
Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and -structures
Yunnan Li, Yunhe Sheng, Rong Tang
In this paper, we study relative Rota-Baxter operators of weight on groups and give various examples. In particular, we propose different approaches to study Rota-Baxter operat…
Symplectic structure, product structures and complex structures on Leibniz algebras
Rong Tang, Nanyan Xu, Yunhe Sheng
In this paper, a symplectic structure on a Leibniz algebra is defined to be a {\em symmetric} nondegenerate bilinear form satisfying certain compatibility condition, and a phase sp…