The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach
Piotr Dowbor ; Andrzej Mróz
Colloquium Mathematicae, Tome 107 (2007), p. 221-261 / Harvested from The Polish Digital Mathematics Library
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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)=(mX)X∈∈ℕ such that M≅⨁X∈XmX 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).

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:283433 
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     year = {2007},
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Piotr Dowbor; Andrzej Mróz. The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach. Colloquium Mathematicae, Tome 107 (2007) pp. 221-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-2-4/