5 citations · 11 across the 12 of their papers we have counts for
12 papers
Cohomology for Deformation maps on quasi-twilled Lie triple systems
Jia Zhao
Due to the importance of invariant, in the present paper, we provide a unified approach to study various kinds of operators on Lie triple systems such as crossed homomorphisms, rel…
Maurer-Cartan characterization, -algebras, and cohomology of relative Rota-Baxter operators on Lie-Yamaguti algebras
Jia Zhao, Yu Qiao
In this paper, we first construct a differential graded Lie algebra that controls deformations of a Lie-Yamaguti algebra. Furthermore, a relative Rota-Baxter operator on a Lie-Yama…
Post Lie-Yamaguti algebras, relative Rota-Baxter operators of nonzero weights, and their deformations
Jia Zhao, Senrong Xu, Yu Qiao
In this paper, we introduce the notions of relative Rota-Baxter operators of weight on Lie-Yamaguti algebras, and post-\LYA s, which is an underlying algebraic structure of rel…
Cohomology and deformations of crossed homomorphisms between Lie-Yamaguti algebras
Jia Zhao, Yu Qiao, Senrong Xu
In this paper, we introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomolo…
Para-Kähler and pseudo-Kähler structures on Lie-Yamaguti algebras
Jia Zhao, Yuqin Feng, Yu Qiao
For a pre-Lie-Yamaguti algebra , by using its sub-adjacent Lie-Yamaguti algebra , we are able to construct a semidirect product Lie-Yamaguti algebra via a representation of…
The classical Lie-Yamaguti Yang-Baxter equation and Lie-Yamaguti bialgebras
Jia Zhao, Yu Qiao
In this paper, we develop the bialgebra theory for Lie-Yamaguti algebras. For this purpose, we exploit two types of compatibility conditions: local cocycle condition and double con…
Cohomology and relative Rota-Baxter-Nijenhuis structures on LieYRep pairs
Jia Zhao, Yu Qiao
A LieYRep pair consists of a Lie-Yamaguti algebra and its representation. In this paper, we establish the cohomology theory of LieYRep pairs and characterize their linear deformati…
Cohomology and deformations of Relative Rota-Baxter operators on Lie-Yamaguti algebras
Jia Zhao, Yu Qiao
In this paper, we establish the cohomology of relative Rota-Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then we use this type of cohomology to characteri…
Relative Rota-Baxter operators and symplectic structures on Lie-Yamaguti algebras
Yunhe Sheng, Jia Zhao
In this paper, first we introduce the notion of a quadratic Lie-Yamaguti algebra and show that the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphis…
Eigenvalues of Laplace operators on non-bipartite graphs
Hongjun Wang, Hongmei Song, Jia Zhao
This paper considers the comparison between the eigenvalues of Laplace operators with the standard conditions and the anti-standard conditions on non-bipartite graphs which are equ…
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs
Peter Kuchment, Jia Zhao
In some previous works, the analytic structure of the spectrum of a quantum graph operator as a function of the vertex conditions and other parameters of the graph was established.…
Eigenvalues of Sturm-Liouville Operators with Distributional Potentials
Jun Yan, Guoliang Shi, Jia Zhao
We introduce a novel approach for dealing with eigenvalue problems of Sturm-Liouville operators generated by the differential expression \begin{equation*} Ly=\frac{1}{r}\left( -(p\…