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Title
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Qurves and quivers
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Author
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Abstract
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| In this paper we associate to a View the MathML source-qurve A (formerly known as a quasi-free algebra [J. Cuntz, D. Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995) 251289] or formally smooth algebra [M. Kontsevich, A. Rosenberg, Noncommutative smooth spaces, math.AG/9812158, 1998]) the one-quiver Q1(A) and dimension vector α1(A). This pair contains enough information to reconstruct for all View the MathML source the GLn-étale local structure of the representation scheme repnA. In an appendix we indicate how one might extend this to qurves over non-algebraically closed fields. Further, we classify all finitely generated groups G such that the group algebra kG is a k-qurve. If char(k)=0 these are exactly the virtually free groups. We determine the one-quiver setting in this case and indicate how it can be used to study the finite-dimensional representations of virtually free groups. As this approach also applies to fundamental algebras of graphs of separable k-algebras, we state the results in this more general setting. |
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Language
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English
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Source (journal)
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Journal of algebra. - New York, N.Y., 1964, currens
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Publication
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New York, N.Y.
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Academic Press
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2005
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ISSN
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0021-8693
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Volume/pages
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290
:2
(2005)
, p. 447-472
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ISI
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000230853100007
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Full text (Publisher's DOI)
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Full text (open access)
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