Fixed rings of generalized Weyl algebras

JOURNAL OF ALGEBRA

卷:536

Article

Gaddis, Jason¹  Won, Robert^2,3 

[1] Miami Univ, Dept Math, 301 S Patterson Ave, Oxford, OH 45056 USA

[2] Wake Forest Univ, Dept Math & Stat, POB 7388, Winston Salem, NC 27109 USA

[3] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

关键词: Generalized Weyl algebras;    Fixed rings;    Filtered group actions;    Auslander's Theorem;   

DOI  :  10.1016/j.jalgebra.2019.06.030

来源: Elsevier

【 摘 要 】

We study actions by filtered automorphisms on classical generalized Weyl algebras (GWAs). In the case of a defining polynomial of degree two, we prove that the fixed ring under the action of a finite cyclic group of filtered automorphisms is again a classical GWA, extending a result of Jordan and Wells. Partial results are provided for the case of higher degree polynomials. In addition, we establish a version of Auslander's theorem for finite cyclic groups of filtered automorphisms acting on classical GWAs. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free