Yangian Algebras and Classical Riemann Problems

Details Yangian Algebras and Classical Riemann Problems Yangian Algebras and Classical Riemann Problems

1997-12-30

arxiv.org/abs/q-alg/9712057v2

Mathematics

Quantum Algebra

36 pages, 3 figures under bezier.sty, corrected some typos

Scientific paper

We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation relations for the deformed algebra of formal currents and the specialization of the Riemann problem for the currents. Two different Riemann problems are considered. They lead to the central extended Yangian double associated with ${sl}_2$ and to the degeneration of scaling limit of elliptic affine algebra. Unless the defining relations for the generating functions of the both algebras coincide their properties and the theory of infinite-dimensional representations are quite different. We discuss also the Riemann problem for twisted algebras and for scaled elliptic algebra.

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