Title 



Qurves and quivers
 
Author 


  
Abstract 



In this paper we associate to a View the MathML sourcequrve A (formerly known as a quasifree 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 onequiver Q1(A) and dimension vector α1(A). This pair contains enough information to reconstruct for all View the MathML source the GLnétale local structure of the representation scheme repnA. In an appendix we indicate how one might extend this to qurves over nonalgebraically closed fields. Further, we classify all finitely generated groups G such that the group algebra kG is a kqurve. If char(k)=0 these are exactly the virtually free groups. We determine the onequiver setting in this case and indicate how it can be used to study the finitedimensional representations of virtually free groups. As this approach also applies to fundamental algebras of graphs of separable kalgebras, we state the results in this more general setting.   
Language 



English
 
Source (journal) 



Journal of algebra.  New York, N.Y.  
Publication 



New York, N.Y. : 2005
 
ISSN 



00218693
 
Volume/pages 



290:2(2005), p. 447472
 
ISI 



000230853100007
 
Full text (Publisher's DOI) 


  
Full text (open access) 


  
