18E30 — 1 articles found.

A Geometrization of the Happel Functor

C. R. Math. Rep. Acad. Sci. Canada Vol. 32 (2) 2010, pp. 52–63
Vol.32 (2) 2010
Fan Xu; Xueqing Chen Details
(Received: 2009-09-27 )
(Received: 2009-09-27 )

Fan Xu, Department of Mathematics, Tsinghua University, Beijing, 100875, P. R. China; email: fanxu@mail.tsinghua.edu.cn

Xueqing Chen, Department of Mathematical, and Computer Sciences, University of Wisconsin–Whitewater, Whitewater, WI 53190 USA; email: chenx@uww.ca

Abstract/Résumé:

The Happel functor is a full and faithful exact functor from the derived category \(\mathcal{D}^b (A)\) of bounded complexes over module category of a finite-dimensional algebra \(A\) to the stable category \(\underline{\operatorname{mod}\,} \hat{A}\) of the repetitive algebra \(\hat{A}\) of \(A\). If \(A\) has finite global dimension, this functor is even an equivalence of triangulated categories. Xiao, Xu, and Zhang defined topological spaces associated with \(\mathcal{D}^b (A)\). In this paper, we attach some topological spaces for \(\underline{\operatorname{mod}\,} \hat{A}\) and construct maps between two kinds of topological spaces as a geometric characterization of the Happel functor.

Le foncteur Happel est un foncteur plein, fidèle, et exact de la categorie derivée \(\mathcal{D}^b (A)\) des complexes bornés sur la categorie des modules d’une algèbre \(A\) de dimension finie dans la categorie stable \(\underline{\operatorname{mod}\,} \hat{A}\) de l’algèbre répétitive \(\hat{A}\) de \(A\). Si \(A\) est de dimension finie (en dimension globale), ce foncteur sera même une équivalence des categories triangulées. Les espaces topologiques associés à \(\mathcal{D}^b (A)\) étaient définés par Xiao, Xu et Zhang. Dans cette article, nous associons quelques espaces topologiques à la categorie \(\underline{\operatorname{mod}\,} \hat{A}\), et nous construisons des applications entre deux sortes des espaces topologiques comme une caractérisation géometrique du foncteur Happel.

Keywords: derived category, repetitive algebra, stable module category

AMS Subject Classification: Derived categories; triangulated categories 18E30

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