Distributivity in lattices of torsion classes over finite-dimensional algebras

2023/03/28 by Luo, Yongle, Wei, Jiaqun
#06D99 #16S90 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2303.15802

Abstract

Let A be a basic finite-dimensional algebra and denote by tors A the collection of all all torsion classes of A. It has been proved in \citeDemonet that tors A is always a completely semidistributive lattice. In the present paper, we investigate the distributivity of this lattice and proved that the lattice is distributive if and only if the algebra is the finite direct product of finite-dimensional local algebras.

Related

• An introduction to the lattice of torsion classes
• Lattices of pretorsion classes
• Minimal inclusions of torsion classes
• Dynamical Combinatorics and Torsion Classes
• Distributive lattices and Auslander regular algebras