广义Kac—Moody代数及其表示性质

Ｂｏｒｃｈｅｒｄｓ在１９８８年首先引入了广义Ｋａｃ－Ｍｏｏｄｙ代数的概念并对其结构和表示做了某些讨论，之后他又研究了广义Ｋａｃ—Ｍｏｏｄｙ代数的中心扩张。Ｋａｃ给出了广义Ｋａｃ—Ｍｏｏｄｙ代数的另一定义，本文先给出了两种广义Ｋａｃ—Ｍｏｏｄｙ代数之间的关系，找出了他们的异同之处，然后讨论了广义Ｋａｃ—Ｍｏｏｄｙ代数中心扩张的某个子代数的一些性质，最后得到了广义Ｋａｃ—Ｍｏｏｄｙ代数上不可约最高权表示权集的一个结果。

GENERALIZED KAC-MOODY ALGEBRAS AND THEIR REPRESENTATION PROPERTIES

In 1988, Borcherds first introduced the concept of generalized Kac-Moody algebras and discussed some properties of their construction and representation furthermore, hestudied centrai extentions of generalized Kac-Moody algebras. Kac gave the other definitionof generalized Kac-Moody algebras. We first indicate the relation between two kinds of gener alized Kac-Moody algebras; moreover, dsicuss some properties of a subalgebras of one central extention of a generalized Kac-Moody algebra. At last, for the irreducible integrablehighest weight module over a generalied Kac-Moody algebra, one result about weight set isobtained.