English

Duality and Boundary Yangians

Quantum Algebra 2007-05-23 v1

Abstract

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 aa 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)).

Keywords

Cite

@article{arxiv.math/9904025,
  title  = {Duality and Boundary Yangians},
  author = {V. D. Lyakhovsky and D. N. Ananikian},
  journal= {arXiv preprint arXiv:math/9904025},
  year   = {2007}
}

Comments

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