广义Kac-Moody代数的根系

The Root System of Generalized Kac-Moody Algebras

本文描述了在一定条件下带有虚单根的广义Kac—Moody代数的根系,证明了其实根系就是某个与其相关的kac-Moody代数的实根系;解决了其虚根系的构造并确定了其生成元的最小个数;此外还确定了只含有一个实单根和一个虚单根的广义Kac-Moody代数的所有根。

The paper studies the root system of generalized Kac-Moody algebras with imaginarysimple roots on the conditions. Its real root system is the real root system of Kac-Moodyalgebras G^R associated with G. The paper also gives an explicit descrpition of the imaginaryroot system of generalized Kac-Moody algebras G, and proves that minimal number ofgenerators. All roots of generalized Kac-Moody algebras only with a real simple root andan imaginary simple root.