湖州师范学院学报
湖州師範學院學報
호주사범학원학보
JOURNAL OF HUZHOU TEACHERS COLLEGE
2014年
10期
8-12
,共5页
W (0,1)代数%中心扩张%导子
W (0,1)代數%中心擴張%導子
W (0,1)대수%중심확장%도자
W (0,1)algebra%central extension%derivation
W(a,b)型李代数是 Witt代数和它的密度张量模的半直积,很多无限维李代数都具有这种结构。这类李代数的结构和表示被广泛的研究。通过计算一类W (0,1)李代数的二维中心扩张P 的导子代数,确定它有四个外导子。在文献[1]中,李代数只有2个外导子,而我们得到了一个李代数的中心扩张的导子代数与其导子代数不同构的例子。
W(a,b)型李代數是 Witt代數和它的密度張量模的半直積,很多無限維李代數都具有這種結構。這類李代數的結構和錶示被廣汎的研究。通過計算一類W (0,1)李代數的二維中心擴張P 的導子代數,確定它有四箇外導子。在文獻[1]中,李代數隻有2箇外導子,而我們得到瞭一箇李代數的中心擴張的導子代數與其導子代數不同構的例子。
W(a,b)형리대수시 Witt대수화타적밀도장량모적반직적,흔다무한유리대수도구유저충결구。저류리대수적결구화표시피엄범적연구。통과계산일류W (0,1)리대수적이유중심확장P 적도자대수,학정타유사개외도자。재문헌[1]중,리대수지유2개외도자,이아문득도료일개리대수적중심확장적도자대수여기도자대수불동구적례자。
W(a,b)Lie algebra is the semi direct product of Witt algebra and its density tensor module.Many infinite dimensional Lie algebras have this algebraic structure.The structure theory and representation theory ofW(a,b)Lie algebra have been investigated by many authors recently.In this pa-per,we calculate the derivations of the Lie algebra P,which are the two dimensional central extensions ofW(0,1).Our study shows that P has four outer derivations.In [1],it is provedW(a,b)Lie algebra has only two outer derivations.Then we obtain one example that the derivation algebra of the central ex-tensions of Lie algebra is not isomorphic to that of the Lie algebra.
