Publicação
Cluster-tilting theory
| dc.contributor.advisor | Marsh, Robert | pt |
| dc.contributor.advisor | Gomes, Catarina Araújo de Santa Clara | pt |
| dc.contributor.author | Simões, Raquel Coelho Guardado | pt |
| dc.date.accessioned | 2010-07-27T08:55:31Z | |
| dc.date.available | 2010-07-27T08:55:31Z | |
| dc.date.issued | 2008 | pt |
| dc.description | Tese de mestado em Matemática (Álgebra, Lógica e Fundamentos) apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2008 | pt |
| dc.description.abstract | Resumo alargado disponível em português | pt |
| dc.description.abstract | The notion of Cluster Algebra first appeared in 2001, in a paper by S. Fomin and A. Zelevinsky, studying the dual canonical basis of the quantum group of a finite dimensional simple Lie algebra over the complex numbers, and also total positivity for algebraic groups. Cluster categories, introduced by A. Buan, R. Marsh, M. Reineke, I. Reiten and G.Todorov [11] in 2004, are certain quotients of the derived category of the module category of a finite dimensional path algebra, and the cluster-tilted algebras, defined by A. Buan, R. Marsh and I. Reiten [8], are the endomorphism algebras of certain objects in a cluster category. Our aim is to study the cluster-tilted algebras associated to a Dynkin quiver of type A, using the graphical definition, involving diagonals of polygons, of the cluster category and its associated cluster-tilted algebras, introduced by P. Caldero, F. Chapoton and R. Schiffler, in 2006. In order to understand the cluster-tilted algebras, we need some background on the theory of representations of algebras (with emphasis on representations of quivers and the Auslander-Reiten theory) and on the theory of cluster algebras (with emphasis on the description of cluster algebras of type A in terms of diagonals and triangulations of a regular polygon and the set of almost positive roots in the root system of type A). | pt |
| dc.format | application/pdf | pt |
| dc.identifier.uri | http://hdl.handle.net/10451/1211 | |
| dc.language.iso | eng | pt |
| dc.subject | Matemática | pt |
| dc.subject | Teses de mestrado | pt |
| dc.title | Cluster-tilting theory | pt |
| dc.type | master thesis | |
| dspace.entity.type | Publication | |
| rcaap.rights | openAccess | pt |
| rcaap.type | masterThesis | pt |