Spectral analysis of finite dimensional algebras and singularities
Spectral analysis of finite dimensional algebras and singularities
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DOI：
10.4171/062
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发表时间：
2008-05
期刊：
影响因子：
--
通讯作者：
H. Lenzing;J. A. Peña
中科院分区：
文献类型：
--
作者：
H. Lenzing;J. A. Peña
对于有限维代数A，有限维A-模的有界导范畴允许Auslander-Reiten三角形，使得Auslander-Reiten平移τ是等价的.在Grothendieck群的水平上，τ诱导了Coxeter变换.更一般地说，这延伸到一个同调有限的三角范畴T承认塞尔对偶。在这两种情况下，Coxeter多项式，也就是Coxeter变换的特征多项式产生A或T的重要同调不变量。光谱分析是对这种相互作用的研究，它经常揭示明显不同的主题之间的意想不到的联系。本文对谱技术进行了综述，并研究了谱技术与奇点理论的联系。特别是，它提供了一个贡献，通过三角范畴自然附着到一个加权射影线的Milnor格的的构造。
For a finite dimensional algebra A of finite global dimension the bounded derived category of finite dimensional A-modules admits Auslander- Reiten triangles such that the Auslander-Reiten translation τ is an equivalence. On the level of the Grothendieck group τ induces the Coxeter transformation �A. More generally this extends to a homologically finite triangulated category T admitting Serre duality. In both cases the Coxeter polynomial, that is, the characteristic polynomial of the Coxeter transformation yields an important homological invariant of A or T. Spectral analysis is the study of this interplay, it often reveals unexpected links between apparently different subjects. This paper gives a summary on spectral techniques and studies the links to singularity theory. In particular, it offers a contribution to the categorifica- tion of the Milnor lattice through triangulated categories which are naturally attached to a weighted projective line.