Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493135 | Journal of Algebra | 2005 | 26 Pages |
Abstract
In this paper we associate to a k-qurve A (formerly known as a quasi-free algebra [J. Cuntz, D. Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995) 251-289] or formally smooth algebra [M. Kontsevich, A. Rosenberg, Noncommutative smooth spaces, math.AG/9812158, 1998]) the one-quiverQ1(A) and dimension vector α1(A). This pair contains enough information to reconstruct for all nâN 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Lieven Le Bruyn,