Constructing Quantized Enveloping Algebras via Inverse Limits of Finite Dimensional Algebras

It is well known that a generalized q-Schur algebra may be constructed as a quotient of a quantized enveloping algebra U or its modified form U̇. On the other hand, we show here that both U and U̇ may be constructed within an inverse limit of a certain inverse system of generalized q-Schur algebras. Working within the inverse limit Û clarifies the relation between U̇ and U. This inverse limit is a q-analogue of the linear dual R[G]∗ of the coordinate algebra of a corresponding linear algebraic group G.