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

• Autorzy: Piotr Dowbor , Andrzej Mróz
• Języki publikacji: EN

Abstrakty

EN

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 $𝒪((dim_{k} M)⁴)$. 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).

Kategorie tematyczne

• 16G20: Representations of quivers and partially ordered sets
• 16G60: Representation type (finite, tame, wild, etc.)
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
• 68Q99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 111
• Numer: 2
• Strony: 221-282

Daty

wydano

2008

Twórcy

autor

Piotr Dowbor

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

Andrzej Mróz

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/cm111-2-6