Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras

It is known that a generalized q-Schur algebra may be constructed as a quotient of a quantized enveloping algebra U or its modified form . On the other hand, we show here that both U and may be constructed within an inverse limit of a certain inverse system of generalized q-Schur algebras. Working within the inverse limit clarifies the relation between 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.