Automorphisms of Generalized Down-Up Algebras

Details Automorphisms of Generalized Down-Up Algebras Automorphisms of Generalized Down-Up Algebras

2007-06-22

arxiv.org/abs/0706.3355v1

Mathematics

Rings and Algebras

20 pages

Scientific paper

A 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,\gamma) 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(\alpha, \beta, \gamma) for which the roots of the polynomial X^2-\alpha X-\beta are not both roots of unity.

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