Graded Automorphism Group of TKK Lie Algebra over Semilattice  

作　　者：Zhang Sheng XIA 

机构地区：[1]School of Sciences, Hubei University for Nationalities, Enshi 445000, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第3期537-544,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 10931006） and Foundation of Educational Department of Hubei Province in China （Grant No. B200529001） The author is grateful to the referee for some helpful suggestions.

摘　　要：Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the Jordan algebra ,：7（S） by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T（J（S））, where S is the ＂smallest＂ semilattice in Euclidean space Rn.Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the Jordan algebra ,：7（S） by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T（J（S））, where S is the ＂smallest＂ semilattice in Euclidean space Rn.

关 键 词：Graded automorphism group TKK Lie algebra SEMILATTICE 

分 类 号：O152.5[理学—数学] O152.7[理学—基础数学]