JEDNOSTKA NAUKOWA KATEGORII A+

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

Tom 107 / 2007

Piotr Dowbor, Andrzej Mróz Colloquium Mathematicum 107 (2007), 221-261 MSC: 16G60, 16G70, 68Q99. DOI: 10.4064/cm107-2-4

Streszczenie

Given a module $M$ over an algebra ${\mit\Lambda}$ and a complete set ${\cal{X}}$ of pairwise nonisomorphic indecomposable ${\mit\Lambda}$-modules, the problem of determining the vector $ m(M)=(m_X)_{X\in {\cal{X}}}\in {\mathbb N}^{\cal{X}}$ such that $M\cong \bigoplus_{X\in \cal {X}}X^{m_X}$ 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 $\widetilde{\mathbb{A}}_{p,q}$. In the second case detailed algorithms are given (Algorithms 4.5 and 5.5).

Autorzy

  • Piotr DowborFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail
  • Andrzej MrózFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek