2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132280A generalization of down-up algebras was introduced by Cassidy and Shelton (J. Algebra 279 (2004), no. 1), the so-called generalized down-up algebras. We describe the automorphism group of conformal Noetherian generalized down-up algebras L(f,r,s,γ) such that r is not a root of unity, listing explicitly the elements of the group. In the last section we apply these results to Noetherian down-up algebras, thus obtaining a characterization of the automorphism group of Noetherian down-up algebras A(α, β, γ) for which the roots of the polynomial X^2-αX-βare not both roots of unity.20 pagesRings and AlgebrasRepresentation Theory16W20, 16S30, 17B37text