6 papers · 1 filter
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…
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…
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…