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arXiv · 0709.2469

Estimate of the number of one-parameter families of modules over a tame algebra

Thomas Brüstle·Vladimir V. Sergeichuk
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Abstract

The problem of classifying modules over a tame algebra A reduces to a block matrix problem of tame type whose indecomposable canonical matrices are zero- or one-parameter. Respectively, the set of nonisomorphic indecomposable modules of dimension at most d divides into a finite number f(d,A) of modules and one-parameter series of modules. We prove that the number of m-by-n canonical parametric block matrices with a given partition into blocks is bounded by 4^s, where s is the number of free entries (which is at most mn), and estimate the number f(d,A).

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BibTeXRIS

Thomas Brüstle, Vladimir V. Sergeichuk. 2007-09-16. Estimate of the number of one-parameter families of modules over a tame algebra. https://doi.org/10.1016/s0024-3795(02)00402-0

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