Congenial algebras: Extensions and examples. Issue 10 (3rd October 2019)

• Record Type: Journal Article
• Authors: Gaddis, Jason; Yee, Daniel
• Is Part Of: Communications in algebra. Volume 47:Issue 10(2019)
• Page Start: 4347
• Page End: 4357
• Publication Date: 2019-10-03
• Subjects: Congenial algebras -- pertinency -- Auslander theorem -- Lie superalgebras; 16E65 -- 16W70 -- 16W22 -- 17B35; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1588976
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: We study the congeniality property of algebras, as defined by Bao, He, and Zhang, to establish a version of Auslander's theorem for various families of filtered algebras. It is shown that the property is preserved under homomorphic images and tensor products under some mild conditions. Examples of congenial algebras in this paper include enveloping algebras of Lie superalgebras, iterated differential operator rings, quantized Weyl algebras, down-up algebras, and symplectic reflection algebras.