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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Degeneration of A-infinity modules


Authors: Bernt Tore Jensen, Dag Madsen and Xiuping Su
Journal: Trans. Amer. Math. Soc. 361 (2009), 4125-4142
MSC (2000): Primary 18E30; Secondary 14L30, 16G10
Published electronically: February 23, 2009
MathSciNet review: 2500881
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Abstract: In this paper we use $ A_{\infty}$-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising $ A_{\infty}$-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Zwara and Riedtmann for modules.


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Additional Information

Bernt Tore Jensen
Affiliation: Institutt for matematiske fag, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway
Address at time of publication: Institut de Mathematique de Jussieu, UMR 7586, 175 Rue Chevaleret, 75013 Paris, France
Email: berntj@math.ntnu.no

Dag Madsen
Affiliation: Institutt for matematiske fag, Norwegian University of Science and Technology, NO–7491 Trondheim, Norway
Address at time of publication: Department of Mathematics, Syracuse University, 215 Carnegie Hall, Syracuse, New York 13244
Email: dagma@math.ntnu.no

Xiuping Su
Affiliation: Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
Address at time of publication: Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom
Email: xsu@math.uni-koeln.de

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04693-5
PII: S 0002-9947(09)04693-5
Keywords: A-infinity modules, degeneration (orbit closure), derived categories
Received by editor(s): May 29, 2007
Published electronically: February 23, 2009
Additional Notes: This research was supported by the European Research Training Network LIEGRITS (MRTN-CT-2003-505078). This work was partly done during a visit at the Université de Sherbrooke. All three authors wish to thank the representation theory group in Sherbrooke for their hospitality. The third author would like to thank the Swiss Science Foundation for financial support during her stay at the University of Berne 2005/2006.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.