Positivity in cluster algebras and its relations with categorifications of cluster algebras and total positivity in semisimple algebraic groups

簇代数中的正性及其与簇代数分类和半单代数群中总正性的关系

• 批准号: 219262073
• 负责人: Professor Dr. Giovanni Cerulli Irelli
• 金额: --
• 依托单位: Dipartimento di Scienze di Base e Applicate per lIngegneria
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/219262073?language=en
• 关键词: Positivity; cluster; algebras; its; relations

In every cluster algebra there is a natural notion of positivity, first noticed by Sherman and Zelevinsky. This project has two main objectives: on one hand investigate this notion in relation with the well–known notion of total positivity in semisimple algebraic groups, in the case when the cluster algebra is the coordinate ring of the corresponding group. On the other hand, our aim is to interpret the positive elements in the language of categorification of the cluster algebra theory. The final goal is to be able to give an explicit, satisfactory answer to the following question: are cluster algebras and their categorifications the right framework to study total positivity?

在每一个簇代数中，都有一个自然的积极性概念，这是谢尔曼和泽列文斯基首先注意到的。这个项目有两个主要目标：一方面，研究这个概念与半单代数群中的全正性概念的关系，在簇代数是相应群的坐标环的情况下。另一方面，我们的目的是解释集群代数理论的范畴化语言中的积极因素。最终的目标是能够给出一个明确的，令人满意的回答以下问题：是集群代数和它们的代数的正确框架来研究总的积极性？