阶化平移Toroidal李代数L_4的导子和泛中心扩张  

The Derivations and Universal Central Extension of Gradation Shifting Toroidal Lie Algebra L_4

作　　者：孔小丽[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2009年第3期305-309,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10671160)资助

摘　　要：Toroidal李代数(加适当的中心和导子)是以Laurent多项式代数为坐标环面的扩张仿射李代数.阶化平移to-roidal李代数Ln(n≥3)是B型和D型toroidal李代数的自然推广.考虑n=4时的导子和泛中心扩张,给出L4的导子,并通过一类特殊的阶化给予证明.也给出L4的所有的2-上循环,从而得到它的泛中心扩张.可以看出结论与孔和谭文章中n≠4时有很大的不同.It is known that toroidal Lie algbras （with certain central elements and derivations added） are extended affine Lie algebra with Laurent polynomial algebra as coordinate torus. Gradation shifting toroidal Lie algebras Ln （n≥3） are generalizations of the toroidal Lie algebras of type B and D. In this paper,the case for n=4 was considered. The derivations of L4 were given,and the result was proved by using a new gradation. The universal central extension of L4 by finding all 2-cocycles was also got. These results are very different from the cases for n≠4 in Kong and Tan＇s paper.

关 键 词：阶化平移toroidal李代数 导子 泛中心扩张 

分 类 号：O152.5[理学—数学]