Thick subcategories of derived categories of gentle algebras
Callum Page
TL;DR
This paper characterizes thick subcategories of derived categories of gentle algebras, showing they are generated by string or band objects, with a bijection between string-generated subcategories and non-crossing paths in a geometric model.
Contribution
It provides a complete classification of thick subcategories in derived categories of gentle algebras, linking algebraic and geometric structures.
Findings
Thick subcategories are generated by string or band objects.
Thick subcategories from string objects correspond to non-crossing paths.
The classification establishes a bijection between algebraic and geometric models.
Abstract
We study thick subcategories of derived categories of gentle algebras. Any thick subcategory of a derived category of a gentle algebra is generated by a set of string objects or a set of band objects. We show the thick subcategories generated by string objects are in bijection with sets of non-crossing paths on the geometric model of the derived category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology