Abstract
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.
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