The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach

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

Abstrakty

EN

Given a module M over an algebra Λ and a complete set 𝓧 of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector $m(M) = (m_X)_{X∈ 𝓧} ∈ ℕ ^{𝓧}$ such that $M ≅ ⨁ _{X∈ 𝓧} X^{m_X}$ is studied. A general method of finding the vectors m(M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed and applied in practice for two classes of algebras: string algebras of finite representation type and hereditary algebras of type $𝔸̃_{p,q}$. In the second case detailed algorithms are given (Algorithms 4.5 and 5.5).

Kategorie tematyczne

• 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: 2007
• Tom: 107
• Numer: 2
• Strony: 221-261

Daty

wydano

2007

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/cm107-2-4