Spherical subcategories in representation theory
Andreas Hochenegger, Martin Kalck, David Ploog
TL;DR
The paper introduces a new invariant for triangulated categories based on the poset of spherical subcategories, providing explicit descriptions for certain algebraic cases and deriving numerical invariants.
Contribution
It defines the poset of spherical subcategories as a new invariant and describes its structure for derived categories of specific finite-dimensional algebras.
Findings
Defined the poset of spherical subcategories and its invariants
Explicitly described spherical subcategories for certain algebras
Computed numerical invariants like cardinality and height
Abstract
We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe spherical subcategories and their poset structure for derived categories of certain finite-dimensional algebras.
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