Mutation and torsion pairs
LA Hügel, R Laking, J Šťovíček, J Vitória - arXiv preprint arXiv:2201.02147, 2022 - arxiv.org
Mutation of compact silting objects is a fundamental operation in the representation theory of
finite-dimensional algebras due to its connections to cluster theory and to the lattice of …
finite-dimensional algebras due to its connections to cluster theory and to the lattice of …
Wide coreflective subcategories and torsion pairs
LA Hügel, F Sentieri - arXiv preprint arXiv:2304.00845, 2023 - arxiv.org
We revisit a construction of wide subcategories going back to work of Ingalls and Thomas.
To a torsion pair in the category $ R\operatorname {-}\operatorname {mod} $ of finitely …
To a torsion pair in the category $ R\operatorname {-}\operatorname {mod} $ of finitely …
Torsion pairs via the Ziegler spectrum
LA Hügel, R Laking, F Sentieri - arXiv preprint arXiv:2403.00475, 2024 - arxiv.org
We establish a bijection between torsion pairs in the category of finite-dimensional modules
over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the …
over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the …
A brick version of a theorem of Auslander
F Sentieri - Nagoya Mathematical Journal, 2023 - cambridge.org
A BRICK VERSION OF A THEOREM OF AUSLANDER Page 1 Nagoya Math. J., 249 (2023),
88–106 DOI 10.1017/nmj.2022.22 A BRICK VERSION OF A THEOREM OF AUSLANDER …
88–106 DOI 10.1017/nmj.2022.22 A BRICK VERSION OF A THEOREM OF AUSLANDER …
Large Bricks and Join-irreducible torsionfree classes
F Sentieri - arXiv preprint arXiv:2405.05635, 2024 - arxiv.org
We show that every join-irreducible torsionfree class in the category of finitely generated
modules over an artinian ring is cogenerated by a single (not necessarily finitely generated) …
modules over an artinian ring is cogenerated by a single (not necessarily finitely generated) …
On large and small torsion pairs
F Sentieri - 2022 - iris.unitn.it
Torsion pairs were introduced by Dickson in 1966 as a generalization of the concept of
torsion abelian group to arbitrary abelian categories. Using torsion pairs, we can divide …
torsion abelian group to arbitrary abelian categories. Using torsion pairs, we can divide …