290 citations · 1.2k across the 89 of their papers we have counts for
14 papers · 1 filter
Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators
Shuai Hou, Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a twilled 3-Lie algebra, and construct an -algebra, whose Maurer-Cartan elements give rise to new twilled 3-Lie algebras b…
Integration and geometrization of Rota-Baxter Lie algebras
Li Guo, Honglei Lang, Yunhe Sheng
This paper first introduces the notion of a Rota-Baxter operator (of weight ) on a Lie group so that its differentiation gives a Rota-Baxter operator on the corresponding Lie al…
The controlling -algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
Yunhe Sheng, Rong Tang, Chenchang Zhu
In this paper, we first construct the controlling algebras of embedding tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and an -algebra respect…
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…
Categorification of VB-Lie algebroids and VB-Courant algebroids
Yunhe Sheng
In this paper, first we introduce the notion of a $\VB$-Lie -algebroid, which can be viewed as the categorification of a $\VB$-Lie algebroid. The tangent prolongation of a Lie $…
Deformations of relative Rota-Baxter operators on Leibniz algebras
Rong Tang, Yunhe Sheng, Yanqiu Zhou
In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations o…
Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation
Yuwang Hu, Jiefeng Liu, Yunhe Sheng
In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a…
Noncommutative Poisson bialgebras
Jiefeng Liu, Chengming Bai, Yunhe Sheng
In this paper, we introduce the notion of a noncommutative Poisson bialgebra, and establish the equivalence between matched pairs, Manin triples and noncommutative Poisson bialgebr…
Cohomologies, extensions and deformations of differential algebras with any weights
Li Guo, Yunnan Li, Yunhe Sheng +1
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has…
Koszul-Vinberg structures and compatible structures on left-symmetric algebroids
Qi Wang, Jiefeng Liu, Yunhe Sheng
In this paper, we introduce the notion of Koszul-Vinberg-Nijenhuis structures on a left-symmetric algebroid as analogues of Poisson-Nijenhuis structures on a Lie algebroid, and sho…
F-manifold algebras and deformation quantization via pre-Lie algebras
Jiefeng Liu, Yunhe Sheng, Chengming Bai
The notion of an F-manifold algebra is the underlying algebraic structure of an -manifold. We introduce the notion of pre-Lie formal deformations of commutative associative alge…
Linearization of the higher analogue of Courant algebroids
Honglei Lang, Yunhe Sheng
In this paper, we show that the spaces of sections of the -th differential operator bundle $\dev^n E$ and the -th skew-symmetric jet bundle $\jet_n E$ of a vector bundle …
Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids
Jiefeng Liu, Yunhe Sheng
In this paper, we construct a homotopy Poisson algebra of degree 3 associated to a split Lie 2-algebroid, by which we give a new approach to characterize a split Lie 2-bialgebroid.…