Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras

Details Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras

2007-11-17

arxiv.org/abs/0711.2764v3

Mathematics

Quantum Algebra

18 pages; to appear in J. Algebra

Scientific paper

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

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