The multiplicity problem for indecomposable decompositions of modules over domestic canonical algebras
P Dowbor, A Mróz - Colloquium Mathematicum, 2008 - infona.pl
P Dowbor, A Mróz
Colloquium Mathematicum, 2008•infona.plGiven 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 …
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 …
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 such that is studied. A precise formula for , 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 for postprojective roots x ∈ X is given (Algorithms 6.1, 6.2 and 6.3).
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