Cluster categories

By I. Reiten. 2010

61 citations recorded by the source corpus.

Cluster algebras were introduced by Fomin-Zelevinsky in 2002 in order to give a combinatorial framework for phenomena occurring in the context of algebraic groups. Cluster algebras also have links to a wide range of other subjects, including the representation theory of finite dimensional algebras, as first discovered by MarshReineke-Zelevinsky. Modifying module categories over hereditary algebras, cluster categories were introduced in work with Buan-Marsh-Reineke-Todorov in order to “categorify” the essential ingredients in the definition of cluster algebras in the acyclic case. They were shown to be triangulated by Keller. Related work was done by Geiss-LeclercSchröer using preprojective algebras of Dynkin type. In work by many authors there have been further developments, leading to feedback to cluster algebras, new interesting classes of finite dimensional algebras, and the investigation of categories of Calabi-Yau dimension 2.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fb2c1a109a5a401d82b2ea21927afa0afd2506b2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. K. Yamagata
2. Thomas Brustle
3. Sophie Morier-Genoud
4. Andrzej Skowronski
5. Dong Yang
6. Sotaro Asai
7. Osamu Iyama
8. B. Keller

In Discrete Mathematics and Combinatorics

1. Thomas Brustle
2. K. Yamagata
3. Sophie Morier-Genoud
4. Andrzej Skowronski
5. Dong Yang

In Geometry and Topology

1. K. Yamagata
2. Andrzej Skowronski
3. Thomas Brustle
4. Sophie Morier-Genoud
5. Dong Yang
6. Sotaro Asai
7. Osamu Iyama
8. B. Keller

Citations in the corpus

• Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics (2015, methodology): “It is more convenient to use the cluster category CQ; see [20, 73].”
• Representations of Algebras and Related Topics (2011, background): “g, we will not discuss cluster algebras and their precise links with representation theory, but we will concentrate on the link between certain categories and quiver mutation. We refer to [67], [25], [82] for nice overviews of categorifications of cluster algebras. Example 1.2. 2 =˚˚ === = 2 2 2 2 1 ”
• Ordered Exchange Graphs (2013, background): “More detailed surveys on some of the objects and maps include [105, 63, 31, 78, 90, 66].”