4 papers
Cohomology theory of Novikov algebras and applications
Pavel Kolesnikov, Yue Li, Yunhe Sheng +1
In this paper, first we give a new characterization of the cohomology of pre-Lie algebras using the Chevalley-Eilenberg cohomology associated to a morphism from the operad of Lie a…
Leibniz -algebras, linear -racks and the Zamolodchikov Tetrahedron equation
Nanyan Xu, Yunhe Sheng
In this paper, first we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2…
The Yang-Baxter equation, Leibniz algebras, racks and related algebraic structures
Nanyan Xu, Yunhe Sheng
The purpose of this paper is to clarify the relations between various constructions of solutions of the Yang-Baxter equation from Leibniz algebras, racks, 3-Leibniz algebras, 3-rac…
Symplectic structure, product structures and complex structures on Leibniz algebras
Rong Tang, Nanyan Xu, Yunhe Sheng
In this paper, a symplectic structure on a Leibniz algebra is defined to be a {\em symmetric} nondegenerate bilinear form satisfying certain compatibility condition, and a phase sp…