n-angulated categories

By C. Geiss, B. Keller, Steffen Oppermann. 2010

154 citations recorded by the source corpus.

Abstract We define n-angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to pre-n-angulations. We obtain a large class of examples of n-angulated categories by considering (n − 2)-cluster tilting subcategories of triangulated categories which are stable under the (n − 2)-nd power of the suspension functor. As an application, we show how n-angulated Calabi–Yau categories yield triangulated Calabi–Yau categories of higher Calabi–Yau dimension. Finally, we sketch a link to algebraic geometry and string theory.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/77319db02de8237584394ce052cc28d762d6a31c

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. Gustavo Jasso
2. Sondre Kvamme
3. Julian Kulshammer
4. Petter Andreas Bergh
5. Marius Thaule

In Geometry and Topology

1. Gustavo Jasso
2. Julian Kulshammer
3. Sondre Kvamme
4. Petter Andreas Bergh
5. Marius Thaule
6. Lidia Angeleri Hugel
7. Thomas Brustle

In Statistical and Nonlinear Physics

1. Sondre Kvamme
2. Julian Kulshammer
3. Petter Andreas Bergh
4. Marius Thaule
5. Gustavo Jasso

Citations in the corpus

• An introduction to higher Auslander–Reiten theory (2016, background): “The intrinsic properties of d-cluster-tilting subcategories have been investigated in [14, 25, 26].”
• n-Abelian and n-exact categories (2014, background): “are isomorphisms for some k ∈ {0,1,...,n +1}. Abusing the terminology, we say that two n-Σ-sequences are weakly isomorphic if they are connected by a finite zigzag of weak isomorphisms. Definition 5.1. [20] A pre-(n + 2)-angulated category is a triple (F,Σ,S) where F is an additive category, Σ: F → F ”
• The axioms for n–angulated categories (2011, methodology): “Note that in [1], it was not explicitly assumed that N be closed under isomorphisms, but it follows implicitly from closure under direct sums.”
• Higher Nakayama algebras I: Construction (2016, background): “luster-tilting subcategory which was introduced by Iyama in [Iya07b]. We recall the denition below as well as the stronger notion of a dZ-cluster-tilting subcategory which is implicit in [Iya11] and [GKO13] in the triangulated case and was introduced in [IJ17] in the abelian case. Denition 1.14. Let”