290 citations · 1.2k across the 89 of their papers we have counts for
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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…
Affine structures on Lie groupoids
Honglei Lang, Zhangju Liu, Yunhe Sheng
Affine structures on a Lie groupoid, including affine -vector fields, -forms and -tensors are studied. We show that the space of affine structures is a 2-vector space…
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Jun Jiang, Satyendra Kumar Mishra, Yunhe Sheng
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Th…
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…
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…