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2010•Journal of Henan University of Science & TechnologyRequires access

Representation of V_q(sl(2)) When q Not a Root of Unity

Cheng Dong

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Abstract

Representations of quantum group Vq(sl(2)) when q is not a root of unity is studied in this paper.Infinite dimensional modules of Vq(sl(2)) when q is not a root of unity are given.All simple modules are determined.It has been proved that,when q is not a root of unity,the actions of generators E and F on finite dimensional modules are nilpotent,and finite dimensional modules of same dimension are isomorphic.

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Representations of quantum group Vq(sl(2)) when q is not a root of unity is studied in this paper.Infinite dimensional modules of Vq(sl(2)) when q is not a root of unity are given.All simple modules are determined.It has been proved that,when q is not a root of unity,the actions of generators E and F on finite dimensional modules are nilpotent,and finite dimensional modules of same dimension are isomorphic.

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Available abstract

Representations of quantum group Vq(sl(2)) when q is not a root of unity is studied in this paper.Infinite dimensional modules of Vq(sl(2)) when q is not a root of unity are given.All simple modules are determined.It has been proved that,when q is not a root of unity,the actions of generators E and F on finite dimensional modules are nilpotent,and finite dimensional modules of same dimension are isomorphic.

Key concepts: Root of unity, Mathematics, Root (linguistics), Dimension (graph theory), Pure mathematics, Nilpotent, Simple module, Simple (philosophy)

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