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Central extension of the Yangian double. (English) Zbl 0887.17007

Alev, J. (ed.) et al., Algèbre non commutative, groupes quantiques et invariants. Septième contact Franco-Belge, Reims, France, June 26–30, 1995. Paris: Société Mathématique de France. Sémin. Congr. 2, 119-135 (1995).
The author describes a construction of a central extension of the Yangian double introduced by himself and V. Tolstoy in a previous paper [Comp. Lett. Math. Phys. (to appear)]. The Yangian is extended by the derivation \(d\) with respect to a spectral parameter, and the double of this extension turns out to be the desired central extension of the Yangian double with the central element \(c\) dual to the derivative \(d\). The details are given in the case of \(sl_2\), and in this case basic representations of the central extension are also studied. The general case is sketched without proof in the last part of the paper.
For the entire collection see [Zbl 0878.00052].

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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