Consistency conditions for brane tilings
Consistency conditions for brane tilings
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DOI：
10.1016/j.jalgebra.2011.05.005
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发表时间：
2011-07-15
影响因子：
0.9
通讯作者：
Davison, Ben
中科院分区：
文献类型：
--
作者：
Davison, Ben
给定一个膜平铺在环面上，我们提供了一种新的方法来证明和推广最近的结果Szendroi，Mozgovic和Reineke关于Donaldson-Thomas理论的模空间的框架循环表示的相关代数。仅利用一个自然的消去型相容性条件，证明了该代数是3-Calabi-Yau，并计算了模空间的Donaldson-Thomas型不变量.两个新的成分，我们的证明是一个等级的代数的路径类别的相关的模关系，和一种方式分配缠绕数对路径的电梯膜平铺的普遍覆盖。这些想法使我们能够将上述结果推广到K（pi，1）曲面上的所有一致膜平铺。我们还证明了一个匡威的：没有一致的膜平铺在一个领域产生一个3-Calabi-Yau代数。(C)2011 Elsevier Inc. All rights reserved.
Given a brane tiling on a torus, we provide a new way to prove and generalise the recent results of Szendroi, Mozgovoy and Reineke regarding the Donaldson-Thomas theory of the moduli space of framed cyclic representations of the associated algebra. Using only a natural cancellation-type consistency condition, we show that the algebras are 3-Calabi-Yau, and calculate Donaldson-Thomas type invariants of the moduli spaces. Two new ingredients to our proofs are a grading of the algebra by the path category of the associated quiver modulo relations, and a way of assigning winding numbers to pairs of paths in the lift of the brane tiling to the universal cover. These ideas allow us to generalise the above results to all consistent brane tilings on K(pi, 1) surfaces. We also prove a converse: no consistent brane tiling on a sphere gives rise to a 3-Calabi-Yau algebra. (C) 2011 Elsevier Inc. All rights reserved.