  The aim of this work is to investigate the structure of some skew twisted
algebras, when the coefficient ring is a localization of the polynomial ring
over the field of characteristic zero, and an involution is provided. A
parallel construction of the rational twisted generalized Weyl algebras is
given. We propose a method and explicit formulas for a constructive description
of these algebras and their involution-symmetric invariant subalgebras based on
the Gelfand-Zeitlin realization of the universal enveloping algebra of some
complex Lie algebras. As concrete examples we discuss special unitary and
orthogonal algebras of rank three.
