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Contracted and expanded integrable structures

Anastasia Doikou and Konstadinos Sfetsos

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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 E2 algebra into sl2 is resolved using the representation theory of the aforementioned quadratic algebras. We also obtain centrally extended algebras associated with rational and trigonometric (q-deformed) R-matrices that are solutions of the Yang–Baxter equation.


PACS

02.30.Rz Integral equations

02.20.Sv Lie algebras of Lie groups

02.30.Tb Operator theory

02.10.Ud Linear algebra

02.10.Yn Matrix theory

MSC

16S30 Universal enveloping algebras of Lie algebras (See mainly 17B35)

20G42 Quantum groups (quantized function algebras) and their representations (See also 16W35, 17B37, 81R50)

16S37 Quadratic and Koszul algebras

Subjects

Mathematical physics

Dates

Issue 47 (27 November 2009)

Received 27 May 2009, in final form 29 September 2009

Published 4 November 2009



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