Duality and Boundary Yangians

Details Duality and Boundary Yangians Duality and Boundary Yangians

1999-04-06

arxiv.org/abs/math/9904025v1

Mathematics

Quantum Algebra

8 pages, LaTex, a report presented at the Workshop SQMQO, Burgos, September 1998

Scientific paper

The existence of dual structures in a Yangian Y(g) signify that the latter belongs to multidimensional naturally parametrized variety of Hopf algebras. These varieties have boundaries containing Yangians Y(a) inequivalent to the original Y(g). The new basic algebra $a$ is an algebra of the cotangent bundle attributed to the dual structure. We show how to construct such boundary Yangians and study some of their properties. We prove that the Hopf algebra Y(a) is a quantization of a parametric solution of the classical Yang-Baxter equation. The limiting procedure and the properties of the boundary Yangians are demonstrated explicitly for the case of Y(sl(2)).

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