-exceptional sequences and the shard intersection order in type A
EJ Hanson - arXiv preprint arXiv:2303.11517, 2023 - arxiv.org
Reading's" shard intersection order" on the symmetric group can be realized as the" lattice of
wide subcategories" of the corresponding preprojective algebra. In this paper, we first use …
wide subcategories" of the corresponding preprojective algebra. In this paper, we first use …
On support τ-tilting graphs of gentle algebras
C Fu, S Geng, P Liu, Y Zhou - Journal of Algebra, 2023 - Elsevier
Let A be a finite-dimensional gentle algebra over an algebraically closed field. We
investigate the combinatorial properties of support τ-tilting graph of A. In particular, it is …
investigate the combinatorial properties of support τ-tilting graph of A. In particular, it is …
A geometric perspective on the -cluster morphism category
arXiv:2302.12217v2 [math.RT] 19 Apr 2023 Page 1 arXiv:2302.12217v2 [math.RT] 19 Apr
2023 A GEOMETRIC PERSPECTIVE ON THE τ-CLUSTER MORPHISM CATEGORY SIBYLLE …
2023 A GEOMETRIC PERSPECTIVE ON THE τ-CLUSTER MORPHISM CATEGORY SIBYLLE …
Two-term silting and -cluster morphism categories
ED Børve - arXiv preprint arXiv:2110.03472, 2021 - arxiv.org
We generalise $\tau $-cluster morphism categories to non-positive proper dg algebras. The
compatibility of silting reduction with support $\tau $-tilting reduction will be an essential …
compatibility of silting reduction with support $\tau $-tilting reduction will be an essential …
Silting reduction and picture categories of 0-Auslander extriangulated categories
ED Børve - arXiv preprint arXiv:2405.00593, 2024 - arxiv.org
Let $\mathcal {C} $ be an extriangulated category and let $\mathcal {R}\subseteq\mathcal
{C} $ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a …
{C} $ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a …
The category of a partitioned fan
M Kaipel - arXiv preprint arXiv:2311.05444, 2023 - arxiv.org
In this paper, we introduce the notion of an admissible partition of a simplicial polyhedral fan
and define the category of a partitioned fan as a generalisation of the $\tau $-cluster …
and define the category of a partitioned fan as a generalisation of the $\tau $-cluster …
A Uniqueness Property of -Exceptional Sequences
Abstract Recently, Buan and Marsh showed that if two complete τ-exceptional sequences
agree in all but at most one term, then they must agree everywhere, provided the algebra is τ …
agree in all but at most one term, then they must agree everywhere, provided the algebra is τ …
Mutating signed-exceptional sequences
AB Buan, BR Marsh - Glasgow Mathematical Journal, 2023 - cambridge.org
We establish some properties of $\tau $-exceptional sequences for finite-dimensional
algebras. In an earlier paper, we established a bijection between the set of ordered support …
algebras. In an earlier paper, we established a bijection between the set of ordered support …
On thick subcategories of the category of projective presentations
M Garcia - arXiv preprint arXiv:2303.05226, 2023 - arxiv.org
We study thick subcategories of the category of 2-term complexes of projective modules over
an associative algebra. We show that those thick subcategories that have enough injectives …
an associative algebra. We show that those thick subcategories that have enough injectives …
-cluster morphism categories of factor algebras
M Kaipel - arXiv preprint arXiv:2408.03818, 2024 - arxiv.org
We take a novel lattice-theoretic approach to the $\tau $-cluster morphism category
$\mathfrak {T}(A) $ of a finite-dimensional algebra $ A $ and define the category via the …
$\mathfrak {T}(A) $ of a finite-dimensional algebra $ A $ and define the category via the …