Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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 Γ 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.

Key words: representations of *-algebras; Temperley-Lieb algebras.

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