Représentations des algèbres et algèbres amassées - Representations of algebras and cluster algebras

Representations des algèbres et algèbres amassées - 代数和簇代数的表示

• 批准号: 41227-2011
• 负责人: Assem, Ibrahim
• 金额: $ 1.89万
• 依托单位: Université de Sherbrooke
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568841
• 关键词: Repr; sentations; des; alg; bres

REPRESENTATIONS OF ALGEBRAS AND CLUSTER ALGEBRAS This project has two facets, closely linked together: (a) The representation theory of finite dimensional algebras. The modern form of the theory goes back to the 1930s, when E. Noether showed that representations may be understood as modules. Thus we study the category of modules over an algebra and the morphisms between them. This theory has undergone a very fast development since the 1970s, thanks to the works of Auslander, Gabriel, Reiten, Ringel and others. We are mostly interested in 3 subdomains of the theory: 1. The study of algebras defined by homological properties. 2. Tilting theory. 3. Hochschild cohomology in relation with simple connectedness. (b) Cluster algebras. Since their introduction 10 years ago by Fomin and Zelevinsky, their study has taken more and more importance and has been related to several areas of mathematics, notably geometry, combinatorics and mathematical physics. Among others, their categorification by Buan, Reiten, Amiot and others has revealed links with the representation theory of algebras, and notably with tilting theory. We are mostly interested in 3 subdomains of the theory: 1. The links with representation theory, in particular with tilting theory. 2. The effective computation of cluster variables. 3. The study of algebras defined by triangulations of surfaces.

代数和簇代数的表示