Moskaleva, Yuliya P.; Samoĭlenko, Yurii S. On transitive systems of subspaces in a Hilbert space. (English) Zbl 1103.47015 SIGMA, Symmetry Integrability Geom. Methods Appl. 2, Paper 042, 19 p. (2006). Let \(H\) be a Hilbert space and \(H_{1},H_{2},\dots,H_{n}\) be \(n\) subspaces of \(H\) and let \(S=(H;H_{1},H_{2},\dots,H_{n})\) denote the system of \(n\) subspaces of the space \(H\). In the paper under review, the authors analyze the complexity of the description problem for transitive systems of subspaces \(S=(H;H_{1},H_{2},\dots,H_{n})\) for \(n \geq 5\). Also, they prove that the problem of describing inequivalent \(*\)-representations of the \(*\)-algebras that give rise to nonisomorphic transitive systems is \(*\)-wild. Reviewer: Ömer Gök (Istanbul) MSC: 47A62 Equations involving linear operators, with operator unknowns 16G20 Representations of quivers and partially ordered sets Keywords:Hilbert spaces; indecomposable system; simultaneously transitive; orthogonal projections; algebras generated by projections; irreducible inequivalent representations; transitive nonisomorphic systems of subspaces PDFBibTeX XMLCite \textit{Y. P. Moskaleva} and \textit{Y. S. Samoĭlenko}, SIGMA, Symmetry Integrability Geom. Methods Appl. 2, Paper 042, 19 p. (2006; Zbl 1103.47015) Full Text: DOI arXiv EuDML EMIS