Work

On Krull-Gabriel dimension of cluster repetitive categories and cluster-tilted algebras

Year: 2024

Type: article

Abstract: Assume that K is an algebraically closed field and denote by KG ( R ) the Krull-Gabriel dimension of R , where R is a locally bounded K -category (or a bound quiver K -algebra). Assume that C is a tilted K -algebra and C ˆ , C ˇ , C ˜ are the associated repetitive category, cluster repetitive category and cluster-tilted algebra, respectively. Our first result states that KG ( C ˜ ) = KG ( C ˇ ) ≤ KG ( C ˆ ) . Since the Krull-Gabriel dimensions of tame locally support-finite repetitive categories are known, we further conclude that KG ( C ˜ ) = KG ( C ˇ ) = KG ( C ˆ ) ∈ { 0 , 2 , ∞ } . Finally, in the Appendix Grzegorz Bobiński presents a different way of determining the Krull-Gabriel dimension of the cluster-tilted algebras, by applying results of Geigle.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2024.107823

Authors: Alicja Jaworska-Pastuszak, Grzegorz Pastuszak, Grzegorz Bobiński

Institution: Nicolaus Copernicus University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,330

Funder: Narodowe Centrum Nauki