一类非极大秩可解完备Lie代数  

Solvable Complete Lie Algebras With Non-maximal Rank

作　　者：姜翠波[1] 杨国庆[1] 

机构地区：[1]烟台师范学院数学系

出　　处：《烟台师范学院学报（自然科学版）》1996年第1期25-28,共4页Yantai Teachers University journal(Natural Science Edition)

摘　　要：证明了给出一个Ｈｅｉｓｅｎｂｅｒｇ代数Ｈ，在同构的意义下存在且仅存在一个以Ｈ为幂零根基的可解完备Ｌｉｅ代数，我们给出了这类完备Ｌｉｅ代数的具体实现，并指出当ｄｉｍＨ＞３时，这类完备Ｌｉｅ代数是非极大秩可解完备Ｌｉｅ代数．In this paper,the authers prove that if H is a Heisenberg algebra,then there exists one and only one up to isomorphism solvable complete Lie algebra whose nilpotent radical is H,and give the realization of this kind of complete Lie algebras. It is pointed out that the solvable complete Lie algebra with nilpntent radical H is a solvable complete Lie algebra with non-maximal raik when dim H>3.

关 键 词：幂零根基 李代数 海森堡代数 可解完备李代数 

分 类 号：O152.5[理学—数学]