290 citations · 1.2k across the 89 of their papers we have counts for
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Representations and cohomologies of relative Rota-Baxter Lie algebras and applications
Jun Jiang, Yunhe Sheng
In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coeffici…
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…
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…
Cohomological characterizations of non-abelian extensions of strict Lie 2-algebras
Rong Tang, Yunhe Sheng
In this paper, we study non-abelian extensions of strict Lie 2-algebras via the cohomology theory. A non-abelian extension of a strict Lie 2-algebra $\g$ by $\frkh$ gives rise to a…
A new approach to representations of -Lie algebras and abelian extensions
Jiefeng Liu, Abdenacer Makhlouf, Yunhe Sheng
In this paper, we introduce the notion of generalized representation of a -Lie algebra, by which we obtain a generalized semidirect product -Lie algebra. Moreover, we develop…
Remarks on Leibniz algebras
Yunhe Sheng, Zhangju Liu
In this paper, first we construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization. Furthermore, we introduce the notion of the naive representation…