量子Yang-Baxter方程的集合解的进展  

Progress on Set-solutions of the Quantum Yang-baxter Equation

作　　者：李志兰[1] 李方[2] 

机构地区：[1]浙江大学农业与生物技术学院,杭州310058 [2]浙江大学理学院,杭州310027

出　　处：《科技通报》2015年第1期1-3,共3页Bulletin of Science and Technology

基　　金：国家自然科学基金(No.11271318);教育部博士点基金(No.20110101110010)

摘　　要：量子Yang-Baxter方程的集合解的问题是一个重要的研究课题[1]。本文在逆半群下对此课题开展研究。对于逆半群S和映射R:S×S→S×S,我们给出了R是量子Yang-Baxter方程的解的充要条件,并据此在Clifford半群情形,给出了量子Yang-Baxter方程的四个集合解。这些解推广了群论意义下的解,是Drinfeld问题研究的一个进展。How to give the set-solutions of the quantum Yang-Baxter equation is an important subject[1]. The aim ofthis paper is to study this subject under inverse semigroups. For an inverse semigroup S and a map R：S ×S→S×S, we give a sufficient and necessary condition for R to be a solution of the quantum Yang-Baxterequation, and then for the case of Clifford semigroups, four set-solutions of the quantum Yang-Baxterequation are obtained. The solutions of the equation under the meaning of groups are generalized. This isan improvement of the study on Drinfeld problem.

关 键 词：Drinfeld问题 量子Yang-Baxter方程 逆半群 CLIFFORD半群 

分 类 号：O152.7[理学—数学] O151.1[理学—基础数学]