Natasha POPOVA and Masha VLASENKO
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv,

On projections with Temperley-Lieb relations

With simple connected graph we associate *-algebra. It is generated by projections with relations of orhogonality or Temperley-Lieb type. We study set of values of parameter for which algebra associated to tree has *-representations. Also we construct the embedding of algebra associated to cycle in algebra of n*n matrices with elements from ring of Laurent polynomials on circle.