论文标题
PBW型的广义二次换向器代数
Generalized quadratic commutator algebras of PBW-type
论文作者
论文摘要
近年来，在量子系统的背景下，已经获得了各种非线性代数结构，作为对称代数，Painlevé超越模型和缺少标签问题。在本文中，我们将所有这些代数视为PBW类型的二次（和高度）换向器支架代数的实例。我们提供了一种简化钻石引理产生的约束的通用方法，并特别应用于对二次情况的全面分析。我们提出了二次代数的新例子，该代数承认立方体Casimir不变。开发了与其他方法（例如Gröbner基础）的联系，我们建议我们的明确和计算技术在其他情况下如何相关。
In recent years, various nonlinear algebraic structures have been obtained in the context of quantum systems as symmetry algebras, Painlevé transcendent models and missing label problems. In this paper we treat all of these algebras as instances of the class of quadratic (and higher degree) commutator bracket algebras of PBW type. We provide a general approach for simplifying the constraints arising from the diamond lemma, and apply this in particular to give a comprehensive analysis of the quadratic case. We present new examples of quadratic algebras, which admit a cubic Casimir invariant. The connection with other approaches such as Gröbner bases is developed, and we suggest how our explicit and computational techniques can be relevant in other contexts.
