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

Piotr Dowbor, and Andrzej Mróz. "The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach." Colloquium Mathematicae 107.2 (2007): 221-261. <http://eudml.org/doc/283433>.

@article{PiotrDowbor2007,
abstract = {Given a module M over an algebra Λ and a complete set of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector $m(M) = (m_X)_\{X∈ \} ∈ ℕ ^\{\}$ such that $M ≅ ⨁ _\{X∈ \} X^\{m_X\}$ 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 $̃_\{p,q\}$. In the second case detailed algorithms are given (Algorithms 4.5 and 5.5).},
author = {Piotr Dowbor, Andrzej Mróz},
journal = {Colloquium Mathematicae},
keywords = {indecomposable modules; string algebras of finite representation type; hereditary algebras; algorithms; representations; decompositions; multiplicity vectors},
language = {eng},
number = {2},
pages = {221-261},
title = {The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach},
url = {http://eudml.org/doc/283433},
volume = {107},
year = {2007},
}

TY - JOUR
AU - Piotr Dowbor
AU - Andrzej Mróz
TI - The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 2
SP - 221
EP - 261
AB - Given a module M over an algebra Λ and a complete set of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector $m(M) = (m_X)_{X∈ } ∈ ℕ ^{}$ such that $M ≅ ⨁ _{X∈ } X^{m_X}$ 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 $̃_{p,q}$. In the second case detailed algorithms are given (Algorithms 4.5 and 5.5).
LA - eng
KW - indecomposable modules; string algebras of finite representation type; hereditary algebras; algorithms; representations; decompositions; multiplicity vectors
UR - http://eudml.org/doc/283433
ER -