收缩和扩张的可积结构
Contracted and expanded integrable structures
摘要：
我们提出了一个通用的框架，以获得某些类型的压缩和中心扩展代数。这是基于存在的二次代数（反射代数和扭曲的杨氏），自然产生的背景下，边界可积模型。利用上述二次代数的表示理论，解决了关于E_2代数“扩张”为s1_2的一个相当古老的误解。我们还获得了中心扩展代数相关的合理和三角（q-变形）R-矩阵的解决方案的杨-巴克斯特方程。
英文摘要：
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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