41 citations · 252 across the 36 of their papers we have counts for
7 papers · 1 filter
Review of deformation theory II: a homotopical approach
Ai Guan, Andrey Lazarev, Yunhe Sheng +1
We give a general treatment of deformation theory from the point of view of homotopical algebra following Hinich, Manetti and Pridham. In particular, we show that any deformation f…
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…
Actions of monoidal categories and representations of Cartan type Lie algebras
Yufeng Pei, Yunhe Sheng, Rong Tang +1
Using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is a left module ca…
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…
Cohomologies of a Lie algebra with a derivation and applications
Rong Tang, Yael Fregier, Yunhe Sheng
The main object of study of this paper is the notion of a LieDer pair, i.e. a Lie algebra with a derivation. We introduce the concept of a representation of a LieDer pair and study…
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…
Leibniz bialgebras, relative Rota-Baxter operators and the classical Leibniz Yang-Baxter equation
Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and Leibniz bialgebras are eq…