On the asymmetry of finite delooping levels

TL;DR

This paper demonstrates that for Artin algebras, the finite delooping level can be asymmetrical on different sides, challenging the assumption of symmetry in such algebraic properties.

Contribution

It introduces a dual construction that alters the delooping level asymmetrically, extending previous work on finite dimensional algebras and rings.

Findings

Finite delooping level is not necessarily symmetric on both sides.

Constructs an algebra that increases delooping level on one side and decreases it on the other.

Extends Cummings' and Krause's work to demonstrate asymmetry in algebraic properties.

Abstract

For any Artin algebra, we construct a related algebra that increases the delooping level on one side while decreasing it to zero on the opposite side. This dual construction corresponds to Cummings' original work on finite dimensional algebras, later extended to rings by Henning Krause. As an application, we show that the finite delooping level is not left-right symmetric.