2024/06/01 by Ruoyu Guo, Guo, Ruoyu
Mathematics · #16E05 #16G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2406.00253
openalex publication_date 2024/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.