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On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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For a class of $*$-algebras, where $*$-algebra $A_{\Gamma,\tau}$ is generated by projections associated with vertices of graph $\Gamma$ and depends on a parameter $\tau$ ($0\tau\leq 1$), we study the sets $\Sigma_\Gamma$ of values of $\tau$ such that the algebras $A_{\Gamma,\tau}$ have nontrivial $*$-representations, by using the theory of spectra of graphs. In other words, we study such values of $\tau$ that the corresponding configurations of subspaces in a Hilbert space exist.
Keywords: representations of $*$-algebras; Temperley–Lieb algebras. 
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Natasha D. Popova; Yurii S. Samoilenko. On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a54/

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