SIGMA 2 (2006), 055, 5 pages math.RT/0605717
On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles
Natasha D. Popova and Yurii S. Samoilenko
Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine
Received December 01, 2005, in final form April 30, 2006; Published online May 29, 2006
For a class of *-algebras, where *-algebra
AΓ,τ is generated by projections associated with
vertices of graph Γ and depends on a parameter τ
(0 < τ ≤ 1), we study the sets ΣΓ of values of
τ such that the algebras AΓ,τ have nontrivial
*-representations, by using the theory of spectra of graphs. In
other words, we study such values of τ that the corresponding
configurations of subspaces in a Hilbert space exist.
representations of *-algebras; Temperley-Lieb algebras.
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