On cosilting hearts over the Kronecker algebra
Alessandro Rapa
TL;DR
This paper studies the structure of hearts derived from torsion pairs in module categories over the Kronecker algebra, focusing on simple objects, atom spectrum, and Gabriel dimension to deepen understanding of their categorical properties.
Contribution
It provides a detailed characterization of simple objects, atom spectrum, and Gabriel dimension in hearts from torsion pairs over the Kronecker algebra, which was previously unexplored.
Findings
Characterization of simple objects in these hearts
Description of the atom spectrum
Computation of Gabriel dimension
Abstract
This paper is about the hearts arising from torsion pairs of finite type in the category of modules over the Kronecker algebra. After a characterization of the simple objects in these hearts, we describe their atom spectrum and compute their Gabriel dimension.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras