Quantum algebras with supersymmetries

该项目旨在量子代数理论方面取得根本性进展。它将发展为显性的 量子代数的主要类的结构和表示理论 量子场论和超对称可积模型。预期结果包括以下解决方案 关于具有超对称的量子代数表示的未决分类问题，它具有 在过去的二十年里一直是开放的。它将涉及到量子理论中新开发的方法 方法和分类都将为数学的发展带来新的数学工具 超对称共形场理论和孤子自旋链模型。

The project aims to make fundamental advances in the theory of quantum algebras. It will develop explicit structure and representation theory of major classes of quantum algebras which are of great importance to quantum field theory and integrable models with supersymmetries. The intended outcomes include a solution of the outstanding classification problem for representations of quantum algebras with supersymmetries, which has remained open for the last two decades. It will involve newly-developed methods within the theory of quantum groups, and both the methods and classification will bring new mathematical instruments for the advance of supesymmetric conformal field theory and soliton spin chain models.