Work

Distributivity in lattices of torsion classes over finite-dimensional algebras

Year: 2025

Type: article

Abstract: Let [Formula: see text] be a basic finite-dimensional algebra and denote by [Formula: see text] the collection of all torsion classes of [Formula: see text]. It has been proved in [L. Demonet, O. Iyama, N. Reading, I. Reiten and H. Thomas, Lattice theory of torsion classes: Beyond [Formula: see text]-tilting theory, Trans. Amer. Math. Soc. Ser. B 10 (2023) 542–612. https://doi.org/10.1090/btran/100 ] that tors [Formula: see text] is always a completely semidistributive lattice. In this paper, we investigate the distributivity of this lattice and prove that the lattice is distributive if and only if the algebra is the finite direct product of finite-dimensional local algebras.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498826502191

Authors: Yongle Luo, Jiaqun Wei

Institutions: Nanjing Normal University, Zhejiang Normal University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Government of Jiangsu Province, Natural Science Foundation of Zhejiang Province

Awards: G3067193249, G45750338, 外部角范畴上的倾斜理论