41 citations · 252 across the 36 of their papers we have counts for
15 papers · 1 filter
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 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…
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…
From relative Rota-Baxter operators and relative averaging operators on Lie algebras to relative Rota-Baxter operators on Leibniz algebras: a uniform approach
Rong Tang, Yunhe Sheng, Friedrich Wagemann
In this paper, first we construct two subcategories (using symmetric representations and antisymmetric representations) of the category of relative Rota-Baxter operators on Leibniz…
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…
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…
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…
Review of deformation theory I: Concrete formulas for deformations of algebraic structures
Ai Guan, Andrey Lazarev, Yunhe Sheng +1
In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie…
Representations and cohomologies of Hom-pre-Lie algebras
Shanshan Liu, Lina Song, Rong Tang
In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie algebras in term of the…
Generalized metric -Leibniz algebras and generalized orthogonal representation of metric Lie algebras
Li-Na Song, Rong Tang
We introduce the notion of a generalized metric n-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric n-Leibniz algebras and faithful gene…
Symplectic, product and complex structures on 3-Lie algebras
Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a phase space of a 3-Lie algebra and show that a 3-Lie algebra has a phase space if and only if it is sub-adjacent to a 3-pre-Lie al…
Cohomologies, deformations and extensions of n-Hom-Lie algebras
Lina Song, Rong Tang
In this paper, first we give the cohomologies of an -Hom-Lie algebra and introduce the notion of a derivation of an -Hom-Lie algebra. We show that a derivation of an -Hom-…
Cohomology characterizations of non-abelian extensions of Hom-Lie algebras
Lina Song, Rong Tang
In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h…
Derivation Hom-Lie 2-algebras and non-abelian extensions of Hom-Lie algebras
Lina Song, Rong Tang
In this paper, we introduce the notion of a derivation of a Hom-Lie algebra and construct the corresponding strict Hom-Lie 2-algebra, which is called the derivation Hom-Lie 2-algeb…