2021/06/09 by Claus Michael Ringel, Ringel, Claus Michael
Mathematics · #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings, Modules, and Algebras #math.RT
paper · pdf · doi:10.48550/arxiv.2106.04924
6 pages
openalex publication_date 2021/06/09 · arxiv created 2022/03/08 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Birge Huisgen-Zimmermann calls a finite dimensional algebra homologically tame provided the little and the big finitistic dimension are equal and finite. The question formulated in the title has been discussed by her in the paper "Representation-tame algebras need not be homologically tame", by looking for any r > 0 at a sequence of algebras Λm with big finitistic dimension r+m. As we will show, also the little finitistic dimension of Λm is r+m. It follows that contrary to her assertion, all her algebras Λm are homologically tame.