Canonical forms of skew polynomial rings

Abstract

We consider special relations in a skew polynomial ring with the following property: every commutation relation between the elements of the ring basis and the elements of the ring of coefficients can be calculated with the help of these special relations. Such relations are called canonical forms of the skew polynomial ring. For example, the Weyl relation is a canonical form for the Weyl algebra. Skew polynomial rings with such canonical forms can be applied, for example, to the representation theory and to mathematical physics. Bibliography: 10 titles.