AFFINE MODULAR LIE-ALGEBRAS

The paper is devoted to the construction of affine Kac-Moody algebras via defining relations arising from an integral affine Cartan matrix, in the case where the ground field has positive characteristic p > 7. Explicit constructions are given for algebras obtained in this way; in distinction with the zero characteristic case they have infinite-dimensional center. A theorem on the universality of this central extension is proved, and a series of finite-dimensional factors of affine modular algebras over the ideals having trivial intersection with Cartan's subalgebra is constructed. Moreover, a construction for the PI-envelopes of affine Kac-Moody algebras is given.