Congenial Algebras: Extensions and Examples

TL;DR

This paper investigates the congeniality property of various algebra classes, demonstrating its preservation under certain operations and providing multiple examples including enveloping algebras and quantized structures.

Contribution

It establishes a version of Auslander's theorem for filtered algebras and shows congeniality is preserved under homomorphic images and tensor products.

Findings

Congeniality is preserved under homomorphic images.

Congeniality is preserved under tensor products.

Examples include enveloping algebras, differential operator rings, and symplectic reflection algebras.

Abstract

We study the congeniality property of algebras, as defined by Bao, He, and Zhang, in order 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.