Qurves and quivers
Qurves and quivers
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屈尔和箭袋
DOI：
10.1016/j.jalgebra.2005.05.012
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发表时间：
2004
影响因子：
0.9
通讯作者：
L. L. Bruyn
中科院分区：
文献类型：
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作者：
L. L. Bruyn
在这篇文章中，我们联系到一个k-曲线A(以前称为拟自由代数[J.Cuntz，D.Quillen，Algebra Expansion and Non Singulity，J.Amer.数学课。SoC。8(1995年)251289]或形式光滑代数[M.Kontsevich，A.Rosenberg，非交换光滑空间，Math.AG/9812158,1998年])1-箭图Q1(A)和维向量α1(A)。该对包含足够的信息来为所有n∈N重构表示方案RepnA的Glnétal型局部结构。在附录中，我们指出了如何将其推广到非代数闭域上的曲线。进一步，我们对所有有限生成的群G进行分类，使得群代数Kg是k-二次曲线。如果char(K)=0，这些就是几乎自由的群。在这种情况下，我们确定了一个箭图设置，并指出它可以用来研究几乎自由群的有限维表示。由于这种方法也适用于可分k-代数的图的基本代数，所以我们在这种更一般的设置下陈述结果。
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 n∈N 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.