12 citations · 36 across the 10 of their papers we have counts for
11 papers
Equivariant Nijenhuis Lie Algebras: Extensions to Classical Lie-Theoretic Structures
Shuai Hou, Zohreh Ravanpak, Yunhe Sheng
We develop a theory of equivariant Nijenhuis Lie algebras (ENL algebras), namely Lie algebras equipped with Nijenhuis operators satisfying an equivariance condition with respect to…
Reynolds Lie bialgebras
Shuai Hou, Maxim Goncharov
In this paper, we establish a bialgebra theory for Reynolds Lie algebras. First we introduce the notion of a quadratic Reynolds Lie algebra and show that it induces an isomorphism…
Deformations and cohomologies of embedding tensors on 3-Lie algebras
Meiyan Hu, Shuai Hou, Lina Song +1
In this paper, first we introduce the notion of an embedding tensor on a 3-Lie algebra, which naturally induces a 3-Leibniz algebra. Using the derived bracket, we construct a Lie 3…
Cohomology and the controlling algebra of crossed homomorphisms on 3-Lie algebras
Shuai Hou, Meiyan Hu, Lina Song +1
In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism fr…
Deformations, cohomologies and abelian extensions of compatible -Lie algebras
Shuai Hou, Yunhe Sheng
In this paper, first we give the notion of a compatible -Lie algebra and construct a bidifferential graded Lie algebra whose Maurer-Cartan elements are compatible -Lie algebr…
-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on -Lie algebras
Shuai Hou, Yunhe Sheng, Yanqiu Zhou
In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on -Lie algebras and -post-Lie algebras. A 3-post-Lie algebra consists of a…
Reynolds -Lie algebras and NS--Lie algebras
Shuai Hou, Yunhe Sheng
In this paper, first we introduce the notion of a Reynolds operator on an -Lie algebra and illustrate the relationship between Reynolds operators and derivations on an -Lie a…
Twisted Rota-Baxter operators on 3-Lie algebras and NS-3-Lie algebras
Shuai Hou, Yunhe Sheng
In this paper, first we introduce the notion of a twisted Rota-Baxter operator on a 3-Lie algebra $\g$ with a representation on . We show that a twisted Rota-Baxter operator ind…
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…
Manin triples of 3-Lie algebras induced by involutive derivations
Shuai Hou, Ruipu Bai
For any -dimensional 3-Lie algebra over a field of characteristic zero with an involutive derivation , we investigate the structure of the 3-Lie algebra $B_1=A\ltimes_{ad…
3-Lie bialgebras and 3-pre-Lie algebras induced by involutive derivations
Ruipu Bai, Shuai Hou, Chuangchuang Kang
In this paper, we study the structure of 3-Lie algebras with involutive derivations. We prove that if is an -dimensional 3-Lie algebra with an involutive derivation , the…