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BULLETIN OF SCIENCE AND TECHNOLOGY
2015年
1期
1-3
,共3页
Drinfeld问题%量子Yang-Baxter方程%逆半群%Clifford半群
Drinfeld問題%量子Yang-Baxter方程%逆半群%Clifford半群
Drinfeld문제%양자Yang-Baxter방정%역반군%Clifford반군
Drinfeld problem%quantum Yang-Baxter equation%inverse semigroup%Clifford semigroup
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。
量子Yang-Baxter方程的集閤解的問題是一箇重要的研究課題[1]。本文在逆半群下對此課題開展研究。對于逆半群S和映射R:S×S→S×S,我們給齣瞭R是量子Yang-Baxter方程的解的充要條件,併據此在Clifford半群情形,給齣瞭量子Yang-Baxter方程的四箇集閤解。這些解推廣瞭群論意義下的解,是Drinfeld問題研究的一箇進展。
양자Yang-Baxter방정적집합해적문제시일개중요적연구과제[1]。본문재역반군하대차과제개전연구。대우역반군S화영사R:S×S→S×S,아문급출료R시양자Yang-Baxter방정적해적충요조건,병거차재Clifford반군정형,급출료양자Yang-Baxter방정적사개집합해。저사해추엄료군론의의하적해,시Drinfeld문제연구적일개진전。
How to give the set-solutions of the quantum Yang-Baxter equation is an important subject[1]. The aim of this 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-Baxter equation, and then for the case of Clifford semigroups, four set-solutions of the quantum Yang-Baxter equation are obtained. The solutions of the equation under the meaning of groups are generalized. This is an improvement of the study on Drinfeld problem.