Exchange Graphs of acyclic Calabi-Yau categories

Details Exchange Graphs of acyclic Calabi-Yau categories Exchange Graphs of acyclic Calabi-Yau categories

2011-09-13

arxiv.org/abs/1109.2924v2

Mathematics

Representation Theory

37 pages, 7 figures

Scientific paper

We study (the principal component of) the oriented exchange graph of hearts in the finite-dimensional derived category D(Gamma_N Q) of the Calabi-Yau-N Ginzburg algebra associated to an acyclic quiver Q. We show that any such heart is induced from some heart in the bounded derived category D(Q) via some `Lagrangian immersion' L:D(Q)->D(Gamma_N Q). Further, we show that the quotient graph by the Seidel-Thomas braid group is the exchange graph for (N-1)-clusters. As an application, we interpret Buan-Thomas' coloured quiver for an (N-1)-cluster in terms of the Ext-quiver of the associated hearts in D(Gamma_N Q).

Affiliated with

Also associated with

No associations

Rating

Exchange Graphs of acyclic Calabi-Yau categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exchange Graphs of acyclic Calabi-Yau categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exchange Graphs of acyclic Calabi-Yau categories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-568386