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.
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.