Symmetry of Derived Delooping Level
arXiv:2406.00253 · doi:10.1007/s10468-025-10355-4
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.
10 pages; corrected mistakes in Lemma 3.2 and Proposition 3.3 pointed out by the referee; This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10468-025-10355-4 Algebr Represent Theor (2025)