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| Titel: |
Tree Matrices and a Matrix Reduction Algorithm of Belitskii |
| Auteur: |
Grzecza, Marcin Kasjan, Stanisław Mróz, Andrzej |
| Verschenen in: |
Fundamenta informaticae |
| Paginering: | Jaargang 118 (2012) nr. 3 pagina's 253-279 |
| Jaar: |
2012-06-08 |
| Inhoud: |
Inspired by the bimodule matrix problem technique and various classification problems in poset representation theory, finite groups and algebras, we study the action of Belitskii algorithm on a class of square n by n block matrices M with coefficients in a field K. One of the main aims is to reduce M to its special canonical form M∞ with respect to the conjugation by elementary transformations defined by a class of matrices chosen in a subalgebra of the full matrix algebra $\mathbb{M}_n$(K). The algorithm can be successfully applied in the study of indecomposable linear representations of finite posets by a computer search using numeric and symbolic computation. We mainly study the case when the di-graph (quiver) associated to the output matrix M∞ of the algorithm is a disjoint union of trees. We show that exceptional representations of any finite poset are determined by tree matrices. This generalizes a theorem of C.M. Ringel proved for linear representations of di-graphs. |
| Uitgever: |
IOS Press |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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