Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv,

UKRAINE

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**

**Abstract:**

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