Kyiv National Taras Shevchenko University,

60 Volodymyrs'ka Str.,

Kyiv-33, 01033 UKRAINE

E-mail: bondarenkoa@ukr.net

**Description of the set of anti-Fock representations
for *-algebras connected with an unimodal mappings**

**Abstract:**

In papers [1, 2] a *C**-algebra connected to a simple non-bijective
dynamical system was constructed. Attempting to construct *C**-algebra
in more general case we start, as in those papers, with description of
the set of representations. The method of description of anti-Fock
representations of the relation *XX**=*f*(*X***X*)
for

continuous unimodal mapping *f* was devised.

**References:**

- Popovych S.V. and Maistrenko T.Yu., $C^*$-algebras, associated with $\mathcal{F}_{2^n}$ unimodal dynamical systems, Ukrainian Math. J., 2001, V.53, N 7, 929-938.
- Bondarenko A.V., Popovych S.V., $C^*$-Algebras Associated with $\mathcal{F}_{2^n}$ Zero Schwarzian Unimodal Mappings, Proceedings of Institute of Mathematics of NAS of Ukraine, 2002, V.43, Part 2, 425-431.