arXiv subjects

Apolonia Gottwald

Publications and source records attributed to Apolonia Gottwald.

2 recordsLinked to original sources

arXiv2018

The Lattice of Subobject Closed Subcategories and Colocal Type

We consider abelian length categories, a generalization of module categories over Artin algebras. Let $\mathcal{A}$ be an abelian length category of colocal type. We show that the lattice $\mathsf{S}(\mathcal{A})$ of full additive subobject closed subcategories of $\mathcal{A}$ is distributive. Furthermore, we give a characterization of abelian length categories of colocal type. If $A$ is an algebra of colocal type over an algebraically closed field, then this characterization is especially simple and we can describe the lattice $\mathsf{S(mod} ~A)$ up to isomorphism.

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arXiv2017

Cofinite Submodule Closed Categories and the Weyl group

We consider hereditary Artin algebras over arbitrary fields and prove that there is a natural bijection between the Weyl groups and the sets of full additive cofinite submodule closed subcategories of the module categories. While Oppermann, Reiten and Thomas have shown this for algebraically closed fields and finite fields, we give a different method of proof that holds independently of the field. In particular, we show a relatively simple way to construct all modules that contain a given preinjective module as a submodule.

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