Extension of a quantized enveloping algebra by a Hopf algebra

摘要: Suppose that H is a Hopf algebra, and $$ \mathfrak{g} $$ generalized Kac-Moody algebra with Cartan matrix A = (a ij )I × I, where I an index set equal to either {1, 2,...,n} or the natural number ℕ. Let f, g be two mappings from G(H), of group-like elements H, such multiplication in {f(i), g(i)|i ∈, I} commutative. Then we define ⊗ U q ( ), ) quantized enveloping .