Resumen de Quantizations of Kac�Moody algebras

V. K. Kharchenko

• We analyze the extent to which a quantum universal enveloping algebra of a Kac�Moody algebra g is defined by multidegrees of its defining relations. To this end, we consider a class of character Hopf algebras defined by the same number of defining relations of the same degrees as the Kac�Moody algebra g. We demonstrate that if the generalized Cartan matrix A of g is connected then the algebraic structure, up to a finite number of exceptional cases, is defined by just one ��continuous�� parameter q related to a symmetrization of A, and one ��discrete�� parameter m related to the modular symmetrizations of A. The Hopf algebra structure is defined by n(n - 1)/2 additional ��continuous�� parameters. We also consider the exceptional cases for Cartan matrices of finite or affine types in more detail, establishing the number of exceptional parameter values in terms of the Fibonacci sequence.