expression for the ladder operators of the ChK-oscillator and extended the Koornwinder’s algebra of differential operators [@N28] to Abelian subalgebra of the ChK-oscillator algebra. In this work we give a complete description of the algebras of sectorial, radial, and boundary oscillators, as well as the construction and study of algebra of two-dimensional ChK-oscillator.

The article has the following structure. In Sec.2, we briefly recall some information on ChK-polynomials of the 2nd type together with some details of construction of the oscillator algebras necessary for us in the following. Below are a few comments regarding the content of Sec.2.

Firstly, we note that the choice of the “coordinate operators” $Z$ and $\overline{Z}$ for sectorial oscillator in Sec.2.2.1 (see formulas -) with the help of recurrence relations is a natural generalization of the corresponding formula for a one-dimensional coordinate operator (see [@N14; @N14a; @N16]).

Construction of the corresponding “momentum operators” $P_Z=Z^\dag$ and $P_{\overline{Z}}=\overline{Z}^\dag$ is performed with the help of the Poisson kernel for the ChK-polynomials and used the method developed in [@N16]. Ladder operators and quadratic Hamiltonian are constructed for operators $Z, \overline{Z}, Z^\dag, \overline{Z}^\dag$ in the standard way. To save space, we omit the unused in this work generalization of the 