The multiplicity problem for indecomposable decompositions of modules over domestic canonical algebras

Piotr Dowbor ; Andrzej Mróz

Colloquium Mathematicae, Tome 111 (2008), p. 221-282 / Harvested from The Polish Digital Mathematics Library

Résumé

Given a module M over a domestic canonical algebra Λ and a classifying set X for the indecomposable Λ-modules, the problem of determining the vector $m(M) = (m_{x})_{x∈X} ∈ ℕ^{X}$ such that $M ≅ ⨁_{x∈X} X_{x}^{m_{x}}$ is studied. A precise formula for $dim_{k} Hom_{Λ}(M,X)$, for any postprojective indecomposable module X, is computed in Theorem 2.3, and interrelations between various structures on the set of all postprojective roots are described in Theorem 2.4. It is proved in Theorem 2.2 that a general method of finding vectors m(M) presented by the authors in Colloq. Math. 107 (2007) leads to algorithms with the complexity $((dim_{k} M)⁴)$. A precise description of algorithms determining the multiplicities $m(M)_{x}$ for postprojective roots x ∈ X is given (Algorithms 6.1, 6.2 and 6.3).

Détail

Publié le : 2008-01-01

Zbl 1185.16020

EUDML-ID : urn:eudml:doc:286364