35 citations · 107 across the 22 of their papers we have counts for
22 papers
Superalgebras and Algebras with Involution: Classifying Cubic Codimension Sequences
Yan-Hong Bao, Jiang-Nan Xu, Yuan-Feng Zhang
A -algebra is either a superalgebra or an algebra with involution. In this paper, we study -ideals associated with unital -algebras whose -codimension…
Codimension sequence, grade, and generating degree: an operadic approach
Y. -H. Bao, D. -X. Fu, J. -N. Xu +4
We study several classes of operadic ideals of the unital associative algebra operad $\uas$. As an application, we classify quotient operads of $\uas$ of GK-dimension . Thi…
Operad and cohomology of associative algebras with generalized derivations
Jiang-Nan Xu, Yan-Hong Bao
An associative algebra with a generalized derivation is called an AsGDer triple. We introduce the operad that encodes AsGDer triples, and prove it is a Koszul operad. Using its Kos…
Ideals of the associative algebra operad
Y. -H. Bao, J. -N. Xu, Y. Ye +2
We prove a one-to-one correspondence between the operadic ideals of the operad $\As$ and -ideals. As a consequence, we show that $\As$ is noetherian and that every proper operad…
On the Cohomology of an associative -operator morphism
Lei Du, Yanhong Bao, Dongxing Fu
Rota-Baxter operators and more generally -operators play a crucial role in broad areas of mathematics and physics, such as integrable systems, the Yang-Baxter equation…
Cohomologies and deformations of coassociative coderivations
Lei Du, Yashuang Ma, Jiangnan Xv +1
The motivation of this paper is to construct a deformation theory of coderivations of coassociative coalgebras. We introduce a notion of a Coder pair, that is, a coassociative coal…
2-unitary Operads of GK-dimension 3
Yan-Hong Bao, Dong-Xing Fu, Yu Ye +1
We study and classify the 2-unitary operads of Gelfand-Kirillov dimension three.
Cohomological invariants of algebraic operads, I
Yan-Hong Bao, Yan-Hua Wang, Xiao-Wei Xu +3
We study various invariants, such as cohomology groups, derivations, automorphisms and infinitesimal deformations, of algebraic operads and show that , $\mathcal{C}c…
Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphs
Yi-Zheng Fan, Yi Wang, Yan-Hong Bao
Unlike an irreducible -matrices, a weakly irreducible -tensor can have more than one eigenvector associated with the least H-eigenvalue. We show that there are…
Eigenvectors of Laplacian or signless Laplacian of Hypergraphs Associated with Zero Eigenvalue
Yi-Zheng Fan, Yi Wang, Yan-Hong Bao +3
Let be a connected -uniform hypergraph. In this paper we mainly consider the eigenvectors of the Laplacian or signless Laplacian tensor of associated with zero eigenvalu…
A Combinatorial Method for Computing Characteristic Polynomials of Starlike Hypergraphs
Yan-Hong Bao, Yi-Zheng Fan, Yi Wang +1
By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the chara…
Truncation of Unitary Operads
Yan-Hong Bao, Yu Ye, James J. Zhang
We introduce truncation ideals of a -linear unitary symmetric operad and use them to study ideal structure, growth property and to classify operads of low Gelfand-Kirillov d…
The Dimension of Eigenvariety of Nonnegative Tensors Associated with Spectral Radius
Yi-Zheng Fan, Tao Huang, Yan-Hong Bao
For a nonnegative weakly irreducible tensor, its spectral radius is an eigenvalue corresponding to a unique positive eigenvector up to a scalar called the Perron vector. But includ…
Eigenvariety of Nonnegative Symmetric Weakly Irreducible Tensors Associated with Spectral Radius and Its Application to Hypergraphs
Yi-Zheng Fan, Yan-Hong Bao, Tao Huang
For a nonnegative symmetric weakly irreducible tensor, its spectral radius is an eigenvalue corresponding to a unique positive eigenvector up to a scalar called the Perron vector.…
The spectral symmetry of weakly irreducible nonnegative tensors and connected hypergraphs
Yi-Zheng Fan, Tao Huang, Yan-Hong Bao +2
Let be a weakly irreducible nonnegative tensor with spectral radius . Let (respectively, ) be the set of normalized…
Restricted Poisson Algebras
Yan-Hong Bao, Yu Ye, James J. Zhang
We re-formulate Bezrukavnikov-Kaledin's definition of a restricted Poisson algebra, provide some natural and interesting examples, and discuss connections with other research topic…
Noncommutative Auslander theorem
Y. -H. Bao, J. -W. He, J. J. Zhang
A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension,…
Pertinency of Hopf actions and quotient categories of Cohen-Macaulay algebras
Y. -H. Bao, J. -W. He, J. J. Zhang
We study invariants and quotient categories of fixed subrings of Artin-Schelter regular algebras under Hopf algebra actions.
A new Frobenius exact structure on the category of complexes
Yan-Fu Ben, Yan-Hong Bao, Xian-Neng Du
Let be an automorphism on an additive category , and let be a natural transformation satisfying for any…
Enveloping Algebras and Cohomology of Leibniz Pairs
Yan-Hong Bao, Yu Ye
We introduce the enveloping algebra for a Leibniz pair, and show that the category of modules over a Leibniz pair is isomorphic to the category of left modules over its enveloping…
Cohomology Structures of A Poisson Algebra: II
Yan-Hong Bao, Yu Ye
We introduce for any Poisson algebra a bicomplex of free Poisson modules, and use it to show that the Poisson cohomology theory introduced in the paper "[M. Flato, M. Gerstenhaber…
On quasi-Poisson Cohomology
Yan-Hong Bao, Yu Ye
Let be a Poisson algebra and $\Q(A)$ its quasi-Poisson enveloping algebra. In this paper, the Yoneda-Ext algebra $\Ext^*_{\Q(A)}(A, A)$, which we call the quasi-Poisson cohomol…