Star product on the Lie coalgebra and its application for calculation of quantum integrals of motion

The article gives an algorithm for constructing quantum integrals of motion on the basis of well-known classic integrals. To construct quantum integrals, we apply star product of the operators' symbols, which is used in the quantization theory. A non-trivial example of the Klein–Fock equation is considered on the four-dimensional Lie group.