Quantum groups in higher genus and Drinfeld's new realizations method ($sl_{2}$ case)

Details Quantum groups in higher genus and Drinfeld's new realizations method ($sl_{2}$ case) Quantum groups in higher genus and Drinfeld's new realizations method ($sl_{2}$ case)

1996-01-21

arxiv.org/abs/q-alg/9601022v1

Mathematics

Quantum Algebra

21 pages

Scientific paper

We define double (central and cocentral) extensions of Manin pairs introduced
by Drinfeld, attached to curves and meromorphic differentials. We define
``infinite twistings'' of these pairs and quantize them in the $sl_{2}$ case,
adapting Drinfeld's ``new realizations'' technique. We study finite dimensional
representations of these algebras in level $0$, and some elliptic examples.

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