Symmetry of Derived Delooping Level

TL;DR

This paper explores the symmetry properties of the derived delooping level, an improved measure related to the finitistic dimension conjecture, and demonstrates its implications for algebraic structures and tensor products.

Contribution

It introduces the derived delooping level, extending the connection to the finitistic dimension conjecture and providing new tools for algebraic analysis.

Findings

Derived delooping level symmetry reduces the finitistic dimension conjecture to algebras with zero derived delooping level.

The paper establishes methods to utilize the derived delooping level for new algebraic results.

Additional work on tensor products of algebras is presented.

Abstract

The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same holds for the derived delooping level, which is an improvement of the delooping level. This reduces the finitistic dimension conjecture to considering algebras whose opposite algebra has (derived) delooping level zero. We thereby demonstrate ways to utilize the new concept of derived delooping level to obtain new results and present additional work involving tensor product of algebras.