arXiv math/06081442006-08math.QAmath.CT

Hall algebras associated to triangulated categories

Jie Xiao, Fan Xu

备注：: 12 pages. Final version, to appear in Duke

英文摘要：

By counting with triangles and the octohedral axiom, we find a direct way to prove the formula of Toën in \cite{Toen2005} for a triangulated category with (left) homological-finite condition.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Remarks on Hall algebras of triangulated categories

We introduce the notion of the Drinfeld dual of an algebra and show that Hall algebras defined by Kontsevich-Soibelman in \cite{KS} are the Drinfeld duals of derived Hall algebras defined in \cite{Toen2005} and \cite{XX2006}. Moreover, we construct the motivic analogue of a derived Hall algebra and prove that it is isomorphic to the motivic Hall algebra constructed in \cite{KS}.

2013-03-17math.CTmath.QA

Enhanced finite triangulated categories

We give a necessary and sufficient condition for the existence of an enhancement of a finite triangulated category. Moreover, we show that enhancements are unique when they exist, up to Morita equivalence.

2020-05-11math.ATmath.CTmath.KT

Hall algebras for odd periodic triangulated categories

We define the Hall algebra associated to any triangulated category under some finiteness conditions with the $t$-periodic translation functor $T$ for odd $t>1.$ This generalizes the results in \cite{Toen2005} and \cite{XX2006}.

2010-01-30math.QAmath.RT

Hall algebras of extriangulated categories

Recently, Nakaoka and Palu introduced a notion of extriangulated categories. This is a unification of exact categories and triangulated categories. In this paper, we generalize the definitions of Hall algebras of exact categories and triangulated categories to extriangulated categories.

2021-08-03math.CTmath.QAmath.RA

Braid cobordisms, triangulated categories, and flag varieties

We argue that various braid group actions on triangulated categories should be extended to projective actions of the category of braid cobordisms and illustrate how this works in examples. We also construct actions of both the affine braid group and the braid cobordism category on the derived category of coherent sheaves on the cotangent bundle to the full flag variety.

2007-05-23math.AGmath.QA