Tree Matrices and a Matrix Reduction Algorithm of Belitskii

• Autorzy: Grzecza M. , Kasjan S. , Mróz A.
• Języki publikacji: EN

Abstrakty

EN

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 \mathbbMn(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.

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 118, nr 3
• Strony: 253--279
• Opis fizyczny: Bibliogr.33 poz.

Twórcy

autor

Grzecza M.

autor

Kasjan S.

autor

Mróz A.

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland,

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