Built on

D. Happel, On the derived category of a finite-dimensional algebra, Comm. Math. Helv
1987
Earlier work this paper cites.
B. Keller, D. Vossieck, Aisles in derived categories, Bull. Soc. Math. Belg
1988
Earlier work this paper cites.
D. Happel, I. Reiten, S.Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc
1996
Earlier work this paper cites.
P. Seidel, R. Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J
2001
Earlier work this paper cites.
M. Khovanov, P. Seidel, Quivers, Floer cohomology and braid group actions, J. Amer. Math. Soc
2002
Earlier work this paper cites.
B. Keller, On triangulated orbit categories, Doc. Math
2005
Earlier work this paper cites.
I. Assem, D. Simson, A. Skowroski, Elements of the Representation Theory of Associative Algebras 1
2006
Earlier work this paper cites.
A. Buan, R.J. Marsh, M. Reineke, I. Reiten, G. Todorov, Tilting theory and cluster combinatorics, Adv. Math
2006
Earlier work this paper cites.

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Then

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2011
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2011

Exchange graphs and Ext quivers

King, Alastair, Qiu, Yu

Understand

We study the oriented exchange graph $\textrm{EG}^\circ(\Gamma_{N}\,Q)$ of reachable hearts in the finite-dimensional derived category $\mathcal{D}(\Gamma_{N}\,Q)$ of the CY-$N$ Ginzburg algebra $\Gamma_{N}Q$ associated to an acyclic quiver $Q$.

We show that any such heart is induced from some heart in the bounded derived category $\mathcal{D}(Q)$ via some `Lagrangian immersion' $\mathcal{L}:\mathcal{D}(Q)\to\mathcal{D}(\Gamma_{N}\,Q)$.
We build on this to show that the quotient of $\textrm{EG}^\circ(\Gamma_{N}\,Q)$ by the Seidel-Thomas braid group is the exchange graph $\textrm{CEG}_{N-1}(Q)$ of cluster tilting sets in the (higher) cluster category $\mathcal{C}_{N-1}(Q)$.
As an application, we interpret Buan-Thomas' coloured quiver for a cluster tilting set in terms of the Ext quiver of any corresponding heart in $\mathcal{D}(\Gamma_{N}\,Q)$.

Built on

D. Happel, On the derived category of a finite-dimensional algebra, Comm. Math. Helv
1987
Earlier work this paper cites.
B. Keller, D. Vossieck, Aisles in derived categories, Bull. Soc. Math. Belg
1988
Earlier work this paper cites.
D. Happel, I. Reiten, S.Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc
1996
Earlier work this paper cites.
P. Seidel, R. Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J
2001
Earlier work this paper cites.
M. Khovanov, P. Seidel, Quivers, Floer cohomology and braid group actions, J. Amer. Math. Soc
2002
Earlier work this paper cites.
B. Keller, On triangulated orbit categories, Doc. Math
2005
Earlier work this paper cites.
I. Assem, D. Simson, A. Skowroski, Elements of the Representation Theory of Associative Algebras 1
2006
Earlier work this paper cites.
A. Buan, R.J. Marsh, M. Reineke, I. Reiten, G. Todorov, Tilting theory and cluster combinatorics, Adv. Math
2006
Earlier work this paper cites.

Similar

T. Bridgeland, Stability conditions on triangulated categories, Ann. Math
2007
Cited alongside, same era.
O. Iyama, Y. Yoshino, Mutation in triangulated categories and rigid Cohen-Macaulay modules, Inv. Math
2008
Cited alongside, same era.
B. Zhu, Generalized Cluster Complexes via Quiver Representations, J. Algebraic Combin
2008
Cited alongside, same era.
C. Amiot, Cluster categories for algebras of global dimension 2 and quivers with potential, Ann. Inst. Fourier
Original
2009
Cited alongside, same era.
A. Buan, H. Thomas, Coloured quiver mutation for higher cluster categories, Adv. Math
Original
2009
Cited alongside, same era.