A5101658727- Advanced Topics in Algebra
- Algebraic structures and combinatorial models
- Homotopy and Cohomology in Algebraic Topology
- Nonlinear Waves and Solitons
- Commutative Algebra and Its Applications
- Rings, Modules, and Algebras
- Advanced Algebra and Geometry
- Advanced Operator Algebra Research
- Finite Group Theory Research
- Fire Detection and Safety Systems
- Face recognition and analysis
- Advanced Combinatorial Mathematics
- Advanced Algebra and Logic
- Advanced Image and Video Retrieval Techniques
- Video Surveillance and Tracking Methods
- Advanced Neural Network Applications
- Sphingolipid Metabolism and Signaling
- Domain Adaptation and Few-Shot Learning
- Advanced Multi-Objective Optimization Algorithms
- AI in cancer detection
- Matrix Theory and Algorithms
- Metaheuristic Optimization Algorithms Research
- Traffic and Road Safety
- Fuzzy and Soft Set Theory
- Sleep and Work-Related Fatigue
Zhejiang Normal University
2014-2025
Hainan University
2022
Changchun University of Science and Technology
2021
Duke University
2021
Zhejiang University of Technology
2021
University of Southern California
2014
University of Washington
2014
Zhejiang University
2007
Nakayama automorphism is used to study group actions and Hopf algebra on Artin-Schelter regular algebras of global dimension three.
We prove that the universal enveloping algebra of a Poisson-Ore extension is length two iterated Ore original algebra. As consequence, we observe certain ring-theoretic invariants algebras are preserved under extensions. apply our results to quadratic Poisson arising from semiclassical limits quantized coordinate rings and family graded structures rank at most two.
It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension an iterated Ore extension. As application, properties are preserved under extensions invariants
The main purpose of this paper is to study a concrete example $\delta$-Koszul algebras, which related three questions raised by Green and Marcos.
In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of algebras in setting. The structures on universal enveloping are discussed.
For a Poisson algebra A, by studying its universal enveloping Ape, we prove duality theorem between homology and cohomology of A.
In this paper, the criteria for minimal Horseshoe Lemma to be true are given via quasi-$δ$-Koszul modules, which nongraded version of $δ$-Koszul modules first introduced by Green and Marcos in 2005. Moreover, some applications also given.
Certain sufficient homological and ring-theoretical conditions are given for a Hopf algebra to have bijective antipode with applications noetherian algebras regarding their behaviors.
The notion of good exact sequence is introduced, which a special class sequences including split as examples. Several criteria characterizing are given. In particular, we prove that the ξ: 0 → K M N if and only Horseshoe Lemma true in "minimal version" with respect to ξ. We also give lot nontrivial examples via "Koszul" objects. Moreover, some applications provided end.
Let A be a Koszul algebra and M finitely generated graded A-module. Suppose that is in degree 0 has pure resolution. We prove that, if rℰ(M) ≠ then Koszul; addition not projective, the converse true as well, where r denotes Jacobson radical of Yoneda [Formula: see text] A, Ext module M.