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n-angulated categories
-
Christof Geiss
,
Bernhard Keller
Published/Copyright:
January 19, 2012
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.
Received: 2010-07-09
Revised: 2011-05-26
Published Online: 2012-01-19
Published in Print: 2013-02
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Curve counting theories via stable objects Ⅱ : DT/ncDT flop formula
- Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions
- n-angulated categories
- Hypertrees, projections, and moduli of stable rational curves
- Locally conformally flat quasi-Einstein manifolds
- Annihilating Selmer modules
- Fitting ideals of ℓ-adic realizations of Picard 1-motives and class groups of global function fields
