|
Degeneration of A-infinity modules
Author(s):
Bernt
Tore
Jensen;
Dag
Madsen;
Xiuping
Su
Journal:
Trans. Amer. Math. Soc.
361
(2009),
4125-4142.
MSC (2000):
Primary 18E30;
Secondary 14L30, 16G10
Posted:
February 23, 2009
MathSciNet review:
2500881
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we use  -modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising  -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.
References:
-
- [ARS]
- M. Auslander, I. Reiten, S. O. Smalø, Representation theory of Artin algebras. Cambridge Studies in Advanced Mathematics, 36. Cambridge University Press, Cambridge, 1997. xiv+425 pp. MR 1476671 (98e:16011)
- [GO'H]
- F. Grünewald, J. O'Halloran, A characterization of orbit closure and applications, J. Algebra 116 (1988), no. 1, 163-175. MR 944153 (89j:17006)
- [H]
- D. Happel, Triangulated categories in the representation theory of finite-dimensional algebras. London Mathematical Society Lecture Note Series, 119. Cambridge University Press, Cambridge, 1988. x+208 pp. MR 935124 (89e:16035)
- [JK]
- G. Janelidze, G. M. Kelly, A note on actions of a monoidal category, Theory Appl. Categ. 9 (2001/02), 61-91 (electronic). MR 1897810 (2003f:18007)
- [JSZ]
- B. T. Jensen, X. Su, A. Zimmermann, Degenerations for derived categories, J. Pure Appl. Algebra 198 (2005), no. 1-3, 281-295. MR 2133687 (2006a:18009)
- [K]
- B. Keller, Introduction to
 -infinity algebras and modules, Homology Homotopy Appl. 3 (2001), no. 1, 1-35. MR 1854636 (2004a:18008a) - [L-H]
- K. Lefèvre-Hasegawa, Sur les
 -catégories, Thèse de Doctorat, Université Paris 7, 2003, arXiv:math.CT/0310337. - [R]
- C. Riedtmann, Degenerations for representations of quivers with relations, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 2, 275-301. MR 868301 (88b:16051)
- [W]
- C. A. Weibel, An introduction to homological algebra. Cambridge Studies in Advanced Mathematics, 38. Cambridge University Press, Cambridge, 1994. xiv+450 pp. MR 1269324 (95f:18001)
- [Y]
- Y. Yoshino, On degeneration of modules, J. Algebra 278 (2004), no. 1, 217-226. MR 2068075 (2005d:16026)
- [Z]
- G. Zwara, Degenerations of finite dimensional modules are given by extensions, Compositio Math. 121 (2000), no. 2, 205-218. MR 1757882 (2001g:14077)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
18E30,
14L30, 16G10
Retrieve articles in all Journals with
MSC (2000):
18E30,
14L30, 16G10
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:
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
Posted:
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.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
