Calabi–Yau triangulated categories

By B. Keller. 2008

156 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/50c8d40a255ebe00e1aee6d82892023093b6515d

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In Computational Theory and Mathematics

Citations in the corpus

The periodicity conjecture for pairs of Dynkin diagrams (2010, unknown): “also [46].”
Dynamical systems and categories (2013, background): “If Q is Dynkin, then DbA is fractional Calabi-Yau, see [31].”
n‐representation‐finite algebras and twisted fractionally Calabi–Yau algebras (2009, methodology): “The Calabi-Yau (CY) property of triangulated categories was introduced by Kontsevich [Ko] (see also [Ke1]).”
A theory of generalized Donaldson–Thomas invariants (2008, background): “By analogy with Definition 7.7, there is also a notion of when a K-linear triangulated category T is 3-Calabi–Yau, discussed in Keller [59].”
Maximal rigid subcategories in 2-Calabi-Yau triangulated categories (2010, background): “If a triangulated category is triangulated equivalent to the stable category of a stably 2−CY exact category, then we call it algebraic 2−CY triangulated category [Ke3].”
n-representation-finite algebras and n-APR tilting (2009, background): “(See [Kel1] or [Kel3] for a motivation for this name.)”
Almost complete cluster tilting objects in generalized higher cluster categories (2010, background): “From the proof given in [18] of lemma 2.”
Auslander–Reiten theory revisited (2008, background): “For n = 2, one can hope that it is given by some generalization of Jacobian algebras of quivers with potentials [50] like 3-CY algebras [45, 64, 93], from the viewpoint of Proposition 3.”
Skew Calabi–Yau algebras and homological identities (2013, background): “See [Ke] for an introductory survey about Calabi-Yau triangulated categories.”
Mutation of cluster-tilting objects and potentials (2008, background): “C(A,B[i]). Then Cis said to be n-Calabi-Yau (n-CY for short) if there is a functorial isomorphism DHom C(A,B) ≃Extn(B,A) for A,B in Cand D = HomK( ,K). Note that this is called weakly n-Calabi-Yau in [K2]. Let Cbe 2-CY. An object T in Cis cluster-tilting if addT = {X ∈C|Ext1 C(T,X) = 0} (see [BMRRT,”