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Quantum groups in higher genus and Drinfeld’s new realizations method (\({\mathfrak sl}_2\) case). (English) Zbl 0897.17012
From the paper: We define double (central and cocentral) extensions of Manin pairs attached to curves and meromorphic differentials, introduced by Drinfeld. We define “infinite twists” 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 at level 0, and some elliptic examples.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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