On the consistency of twisted generalized Weyl algebras. (Q2845852)

Twisted generalized Weyl algebras (TGWA) are multiparameter generalizations of Weyl algebras. The definition of a TGWA, given by \textit{V. Mazorchuk} and \textit{L. Turowska}, [Commun. Algebra 27, No. 6, 2613-2625 (1999; Zbl 0949.17003)], involves a base ring, a collection of automorphisms of this ring and a collection of elements of this ring.NEWLINENEWLINE In the paper under review the authors determine sufficient and necessary conditions (on both the base ring and chosen automorphisms and elements) which guarantee that the corresponding TGWA is a non-trivial ring. In particular, it turns out that the list of conditions proposed in Section 2 of [op. cit.] is not complete and one extra set of conditions is necessary.