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引用次数: 5
摘要
摘要我们介绍并研究了上同调Hall代数$\mathcal的一个费米子过程{H}_{\Pi_Q}$预投影代数的表示,其选择性地将BPS李代数的上同调奇偶性从偶数切换到奇数。我们通过变形降维确定Etingof和Rains工作中研究的预投影代数的中心扩展的上同调Donaldson–Thomas不变量来实现这一点。通过相同的技术,我们确定了Crawley–Boevey和Holland引入的$\unicode{x03BC}$变形预投影代数的表示堆栈的Borel–Moore同调,用于所有维度向量。这提供了Crawley Boevey和Van den Bergh关于变形预投影代数的表示的光滑模方案的上同调的结果的共同推广,以及我先前关于未变形预投影代的表示堆栈的Borel–Moore同调的结论。
A boson-fermion correspondence in cohomological Donaldson–Thomas theory
Abstract We introduce and study a fermionisation procedure for the cohomological Hall algebra
$\mathcal{H}_{\Pi_Q}$
of representations of a preprojective algebra, that selectively switches the cohomological parity of the BPS Lie algebra from even to odd. We do so by determining the cohomological Donaldson–Thomas invariants of central extensions of preprojective algebras studied in the work of Etingof and Rains, via deformed dimensional reduction. Via the same techniques, we determine the Borel–Moore homology of the stack of representations of the
$\unicode{x03BC}$
-deformed preprojective algebra introduced by Crawley–Boevey and Holland, for all dimension vectors. This provides a common generalisation of the results of Crawley-Boevey and Van den Bergh on the cohomology of smooth moduli schemes of representations of deformed preprojective algebras and my earlier results on the Borel–Moore homology of the stack of representations of the undeformed preprojective algebra.
期刊介绍:
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