论文标题
关于等级1 Kac-Moody代数的整体形式
On the integral form of rank 1 Kac-Moody algebras
论文作者
论文摘要
在本文中，我们应证明，drinfeld发电机的分裂功能$ x_r^{\ pm} $的kac-moody代数的$ x_r^{\ pm} $在整数上产生的子词架，该代数的$ a_2^{（2）} $是一个整体形式（严格地比Mitzman的（参见Mitzman的一般化），我们的表现很小，只要[MI] Alla andra afra andra afra of the Inception andra andra of the Broving of the Brovece of Brovece of Broving of the Broving of the affra andra andra andra of the novebra [G]中的花环是无链的仿射kac-moody代数，我们将明确确定换向关系。
In this paper we shall prove that the subalgebra generated over the integers by the divided powers of the Drinfeld generators $x_r^{\pm}$ of the Kac-Moody algebra of type $A_2^{(2)}$ is an integral form (strictly smaller than Mitzman's (see [Mi]) of the enveloping algebra, we shall exhibit a basis generalizing the one provided by Garland in [G] for the untwisted affine Kac-Moody algebras, and we shall determine explicitly the commutation relations. Moreover we prove that both in the untwisted and in the twisted case the positive (respectively negative) imaginary part of the integral form is an algebra of polynomials over the integers.
