3 citations · 10 across the 12 of their papers we have counts for
13 papers
Learning Proposition-Level Links from Sentence-Level Supervision for Neuro-Symbolic NLI
Xuyao Feng, Antonis Bikakis
We study neuro-symbolic natural language inference (NLI) with independently translated propositional representations of the premise and hypothesis. Before symbolic reasoning, the s…
Affine Dual Braid Monoids: Finite Cores, Exceptional Cluster Complexes, and Koszul Resolutions
Jindong Yan, Shenglin Zhu
For every finite-rank crystallographic affine Coxeter system and Coxeter element , we construct a minimal linear graded free resolution of the trivial module over $k[M([…
Standard Polynomials for Principal Subalgebras of Path Algebras
Yihao Zheng, Shenglin Zhu
We investigate standard polynomials for principal subalgebras of path algebras. First, we use standard polynomials to study the -theory of principal subalgebras. Then we descri…
Nilpotent Lie algebras obtained by ordered sets and Ricci solitons
Yihao Zheng, Shenglin Zhu
Nilpotent Lie groups with left-invariant metrics provide nontrivial examples of Ricci solitons. Some typical examples are given by the class of two-step nilpotent Lie algebras obta…
Weak Hopf Algebras, Smash Products and Applications to Adjoint-Stable Algebras
Zhimin Liu, Shenglin Zhu
For a semisimple quasi-triangular Hopf algebra over a field of characteristic zero, and a strongly separable quantum commutative -module algebra ove…
Structures of Adjoint-Stable Algebras over Factorizable Hopf Algebras
Zhimin Liu, Shenglin Zhu
For a quasi-triangular Hopf algebra , there is a notion of transmuted braided group of introduced by Majid. The transmuted braided group is…
Centers of Braided Tensor Categories
Zhimin Liu, Shenglin Zhu
Let be a finite braided multitensor category. Let be Majid's automorphism braided group of , then is a cocommutative Hopf algebra in $\mathcal{C}…
The applications of probability groups on Hopf algebras
Jingheng Zhou, Shenglin Zhu
In this work, we use probability groups, introduced by Harrison in 1979, as a tool to study a semisimple Hopf algebra with a commutative character ring and prove that the algeb…
On the Structure of Irreducible Yetter-Drinfeld Modules over Quasi-Triangular Hopf Algebras
Zhimin Liu, Shenglin Zhu
Let be a finite dimensional semisimple and cosemisimple quasi-triangular Hopf algebra over a field . In this paper, we give the structure of irreducible obj…
On the Exponent of Finite-Dimensional Non-Cosemisimple Hopf Algebras
Kangqiao Li, Shenglin Zhu
In 1999, Y. Kashina introduced the exponent of a Hopf algebra. In this paper, we prove that the exponent of a finite dimensional non-cosemisimple Hopf algebra with Chevalley proper…
Frobenius and Mashke type Theorems for Doi-Hopf modules and entwined modules revisited: a unified approach
Tomasz Brzezinski, S. Caenepeel, G. Militaru +1
We study when induction functors (and their adjoints) between categories of Doi-Hopf modules and, more generally, entwined modules are separable, resp. Frobenius. We present a unif…
Separable functors for Doi-Hopf modules. Applications
S. Caenepeel, B. Ion, G. Militaru +1
There are theorems in the literature which are referred as Maschke type theorems, because of the attempt to generalize Maschke's classical theorem. Our remark is that all these the…
Factorisation structures of algebras and coalgebras
S. Caenepeel, B. Ion, G. Militaru +1
We consider the factorisation problem for bialgebras: when a bialgebra factorises as , where and are algebras and coalgebras (but not necessarly bialgebras). Give…