Konstyantyn YUSENKO
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv,
E-mail: kay@imath.kiev.ua

On infinity of parameters set, for which representations of algebra $\mathcal P_{\Gamma,\chi}$
in case when $\Gamma$ is extended Dynkin diagram exist

For associated with extended Dynkin diagrams $*$-algebras we study conditions under which the set of parameters, for which there are representation, is infinite.