Boyle, Mike; Huang, Danrun Poset block equivalence of integral matrices. (English) Zbl 1028.15006 Trans. Am. Math. Soc. 355, No. 10, 3861-3886 (2003). Given square matrices \(B\) and \(B'\) with a poset-indexed block structure (for which an \(ij\) block is zero unless \(i\preccurlyeq j\)), when are there invertible matrices \(U\) and \(V\) with this required-zero-block structure such that \(UBV= B'\)? The authors give complete invariants for the existence of such an equivalence for matrices over a principal ideal domain \({\mathcal R}\).As one application, when \({\mathcal R}\) is a field one classifies such matrices up to similarity by matrices respecting the block structure. The paper also gives complete invariants for equivalence under the additional requirement that the diagonal blocks of \(U\) and \(V\) have determinant 1. The invariants involve an associated diagram (the “\(K\)-web”) of \({\mathcal R}\)-module homomorphisms. The study is motivated by applications to symbolic dynamics and \(C^*\)-algebras. Reviewer: Rodica Covaci (Cluj-Napoca) Cited in 3 ReviewsCited in 19 Documents MSC: 15A21 Canonical forms, reductions, classification 06A11 Algebraic aspects of posets 06F25 Ordered rings, algebras, modules 15B36 Matrices of integers 16G20 Representations of quivers and partially ordered sets 37B10 Symbolic dynamics 46L35 Classifications of \(C^*\)-algebras Keywords:block equivalence; poset; integer matrix; principal ideal domain; cokernel; flow equivalence; representation; similarity; symbolic dynamics; \(C^*\)-algebras PDFBibTeX XMLCite \textit{M. Boyle} and \textit{D. Huang}, Trans. Am. Math. Soc. 355, No. 10, 3861--3886 (2003; Zbl 1028.15006) Full Text: DOI References: [1] W.A. Adkins and S.H. 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