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

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

2007-09-16

arxiv.org/abs/0709.2469v1

Linear Algebra Appl. 365 (2003) 115-133

Mathematics

Representation Theory

23 pages

Scientific paper

10.1016/S0024-3795(02)00402-0

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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