Contracted and expanded integrable structures

Details Contracted and expanded integrable structures Contracted and expanded integrable structures

2009-04-22

arxiv.org/abs/0904.3437v2

J.Phys.A42:475204,2009

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, Latex. Comments and clarifications added. Version to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/42/47/475204

We propose a generic framework to obtain certain types of contracted and centrally extended algebras. This is based on the existence of quadratic algebras (reflection algebras and twisted Yangians), naturally arising in the context of boundary integrable models. A quite old misconception regarding the "expansion" of the E_2 algebra into sl_2 is resolved using the representation theory of the aforementioned quadratic algebras. We also obtain centrally extended algebras associated to rational and trigonometric (q-deformed) R-matrices that are solutions of the Yang--Baxter equation.

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