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This article is cited in 3 scientific papers (total in 3 papers)
On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles
Natasha D. Popova, Yurii S. Samoilenko Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine
Abstract:
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.
Received: December 1, 2005; in final form April 30, 2006; Published online May 29, 2006
Citation:
Natasha D. Popova, Yurii S. Samoilenko, “On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles”, SIGMA, 2 (2006), 055, 5 pp.
Linking options:
https://www.mathnet.ru/eng/sigma83 https://www.mathnet.ru/eng/sigma/v2/p55
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