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Poisson automorphisms and quiver moduli

Part of: Families, fibrations Representation theory of rings and algebras

Published online by Cambridge University Press:  11 August 2009

Markus Reineke
Markus Reineke
Affiliation:
Fachbereich C, Mathematik, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany (reineke@math.uni-wuppertal.de)
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Abstract

A factorization formula for certain automorphisms of a Poisson algebra associated with a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing formulae for Donaldson–Thomas type invariants of Kontsevich and Soibelman.

Keywords

Donaldson–Thomas invariantsHall algebrasPoisson automorphismsquiver moduli

MSC classification

Secondary: 16G20: Representations of quivers and partially ordered sets 14D20: Algebraic moduli problems, moduli of vector bundles
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 3 , July 2010 , pp. 653 - 667
Copyright
Copyright © Cambridge University Press 2009

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References

1.Bridgeland, T. and Toledano-Laredo, V., Stability conditions and Stokes factors, preprint arXiv:0801.3974 (2008).Google Scholar
2.Engel, J. and Reineke, M., Smooth models of quiver moduli, preprint arXiv:0706.4306 (2007), Math. Z., in press.Google Scholar
3.Gross, M., Pandharipande, R. and Siebert, B., The tropical vertex, preprint arXiv: 0902.0779 (2009).Google Scholar
4.Kontsevich, M. and Soibelman, Y., Stability structures, Donaldson–Thomas invariants and cluster transformations, preprint arXiv:0811:2435 (2008).Google Scholar
5.Reineke, M., Feigin's map and monomial bases for quantized enveloping algebras, Math. Z. 237(3) (2001), 639–667.CrossRefGoogle Scholar
6.Reineke, M., The Harder–Narasimhan system in quantum groups and cohomology of quiver moduli, Invent. Math. 152 (2003), 349–368.CrossRefGoogle Scholar
7.Reineke, M., Moduli of representations of quivers, in Trends in representation theory of algebras and related topics (ed. Skowronski, A.), European Mathematical Society Series of Congress Reports (European Mathematical Society Publishing House, Zürich, 2008).Google Scholar