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Existence and dimensionality of simple weight modules for quantum enveloping algebras

Published online by Cambridge University Press:  17 April 2009

Zhiyong Shi
Zhiyong Shi
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, CanadaN6A 5B7
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We give sufficient and necessary conditions for simple modules of the quantum group or the quantum enveloping algebra Uq(g) to have weight space decompositions, where g is a semisimple Lie algebra and q is a nonzero complex number. We show that

(i) if q is a root of unity, any simple module of Uq(g) is finite dimensional, and hence is a weight module;

(ii) if q is generic, that is, not a root of unity, then there are simple modules of Uq(g) which do not have weight space decompositions.

Also the group of units of Uq(g) is found.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 35 - 40
Copyright
Copyright © Australian Mathematical Society 1993

References

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