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

2003/03/25 by Thomas Brüstle, Vladimir V. Sergeichuk
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RT #msc:15A21 #msc:16G60

paper · pdf · doi:10.1016/s0024-3795(02)00402-0

published as Linear Algebra Appl. 365 (2003) 115-133 · 23 pages

openalex publication_date 2003/03/25 · arxiv created 2007/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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).

Citations

• Canonical matrices for linear matrix problems