Congenial algebras: Extensions and examples

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.

Keywords:

• Congenial algebras
• pertinency
• Auslander theorem
• Lie superalgebras

2010 Mathematics Subject Classification:

• 16E65
• 16W70
• 16W22
• 17B35

Acknowledgments

The authors thank James Zhang for several helpful conversations. They also thank the anonymous referee for a careful reading and for pointing out a simplification of Definition 2.

Additional information

Funding

The first author was partially supported by a grant from the Miami University Senate Committee on Faculty Research.