多分量loop代数及其应用  

Multi-component loop algebra and its applications

作　　者：赵晶[1] 龚新波[2] 

机构地区：[1]大连大学信息工程学院,辽宁大连116622 [2]山东科技大学信息学院,山东青岛255610

出　　处：《辽宁师范大学学报（自然科学版）》2008年第1期34-36,共3页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：利用Lie代数A1的两个子代数间的换位关系,通过线性同构映射,构造了两个相应的多分量Lie代数.根据Lie代数的分次,它们的loop代数的构造方法有多种.本文构造了其中的一类loop代数.作为第一个loop代数应用,得到了AKNS方程族的扩展可积模型.对于第二个loop代数的应用,我们将另文讨论.本文提供的方法可以普遍地应用.By taking use of the commutative relations of two subalgebras of the Lie algebra A1 and linear isomorphic mapping, two corresponding multi-component Lie algebras are constructed. From the gradations of Lie algebra, many methods to construct loop algebra are possible. One of them is given in this paoer. As the first application of the loop algebra, the expanding-integrable model of the AKNS hierarchy of evolution equations is obtained. We shall discuss the second application of the loop algebra in another paper. The method given in the paper can be used to other cases.

关 键 词：LOOP代数 可积模型 AKNS族 

分 类 号：O175.29[理学—数学]