Results 11 to 20 of about 21,122 (292)

Torsion Pairs and Ringel Duality for Schur Algebras [PDF]

Algebras and Representation Theory, 2023
Let A be a finite-dimensional algebra over an algebraically closed field. We use a functorial approach involving torsion pairs to construct embeddings of endomorphism algebras of basic projective A–modules P into those of the torsion submodules of P.
Law, Stacey; id_orcid, Erdmann, Karin
core   +7 more sources

Mutation and torsion pairs [PDF]

Algebra & Number Theory
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 torsion pairs in module or derived categories.
Lidia Angeleri, Jorge Nuno dos Santos Vitoria, Jorge Vitoria, Jan Stovicek, Rosanna Laking, Lidia Angeleri Hügel   +5 more
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Torsion pairs and cosilting in type A ̃

, 2022
Torsion pairs in the category of finitely presented modules over a noetherian ring can be parametrised by the class of cosilting modules. In this paper, we characterise such modules in terms of their indecomposable summands, providing a new approach to ...
Baur, Karin, Laking, Rosanna, Laking, R. ; https://orcid.org/, Baur, K.   +3 more
core   +2 more sources

Torsion pairs in repetitive cluster categories of type $A_n$

Journal of Algebraic Combinatorics, 2023
We give a complete classification of torsion pairs in repetitive cluster categories of type $A_n$, which were defined by Zhu as the orbit categories, via certain configurations of diagonals, called Ptolemy diagrams.
Chang, Huimin
core   +2 more sources

Split t-structures and torsion pairs in hereditary categories [PDF]

Journal of Algebra and Its Applications, 2018
We construct a bijection between split torsion pairs in the module category of a tilted algebra having a complete slice in the preinjective component with corresponding [Formula: see text]-structures.
Sonia Trepode, Assem, Ibrahim, Ibrahim Assem, Souto Salorio, María José, María José Souto-Salorio, Trepode, Sonia Elisabet   +5 more
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On Auslander's formula and cohereditary torsion pairs

Communications in Contemporary Mathematics, 2018
For a small abelian category C, Auslander's formula allows us to express C as a quotient of the category mod - C of coherent functors on C. We consider an abelian category with the added structure of a cohereditary torsion pair tau = (T, F).
Banerjee, Abhishek, Banerjee, A., Abhishek Banerjee   +2 more
core   +4 more sources

On one-sided torsion pair

Science in China Series A: Mathematics, 2007
Motivated by the concept of a torsion pair in a pre-triangulated category induced by Beligiannis and Reiten, the notion of a left (right) torsion pair in the left (right) triangulated category is introduced and investigated.
Xin, Lin, Lin, Ya-nan, 林亚南
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Torsion pairs via the Ziegler spectrum

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 Ziegler spectrum of A and a set I of indecomposable injective A ...
Sentieri, Francesco, Laking, Rosanna, Hügel, Lidia Angeleri   +2 more
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Filtrations and torsion pairs in Abramovich Polishchuk's heart

Peking Mathematical Journal
We study some abelian subcategories and torsion pairs in Abramovich Polishchuk's heart. And we construct stability conditions on a full triangulated subcategory $\mathcal{D}^{\leq 1}_S$ in $D(X\times S)$, for an arbitrary smooth projective variety S.
Liu, Yucheng
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Serre functors and complete torsion pairs

Given a torsion pair $(\mathcal{T},\mathcal{F})$ in an abelian category $\mathcal{A}$, there is a t-structure $(\mathcal{U}_\mathcal{T},\mathcal{V}_\mathcal{T})$ determined by $\mathcal{T}$ on the derived category $D^b(\mathcal{A})$.
He, Ping, Han, Zhe
core   +2 more sources