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pro vyhledávání: '"Hanson, A. J."'
Let $A$ be the path algebra of a quiver of Dynkin type $\mathbb{A}_n$. The module category $\text{mod}\,A$ has a combinatorial model as the category of diagonals in a polygon $S$ with $n+1$ vertices. The recently introduced notion of almost rigid mod
Externí odkaz:
http://arxiv.org/abs/2410.04627
Autor:
Hanson, Eric J.
Let $\Lambda$ be a finite-dimensional basic algebra. Sakai recently used certain sequences of image-cokernel-extension-closed (ICE-closed) subcategories of finitely generated $\Lambda$-modules to classify certain (generalized) intermediate $t$-struct
Externí odkaz:
http://arxiv.org/abs/2410.01963
We introduce a notion of mutation for $\tau$-exceptional sequences of modules over arbitrary finite dimensional algebras. For hereditary algebras, we show that this coincides with the classical mutation of exceptional sequences. For rank two algebras
Externí odkaz:
http://arxiv.org/abs/2402.10301
One of the main objectives of topological data analysis is the study of discrete invariants for persistence modules, in particular when dealing with multiparameter persistence modules. In many cases, the invariants studied for these non-totally order
Externí odkaz:
http://arxiv.org/abs/2402.09190
The pop-stack operator of a finite lattice $L$ is the map $\mathrm{pop}^{\downarrow}_L\colon L\to L$ that sends each element $x\in L$ to the meet of $\{x\}\cup\text{cov}_L(x)$, where $\text{cov}_L(x)$ is the set of elements covered by $x$ in $L$. We
Externí odkaz:
http://arxiv.org/abs/2312.03959
We discuss applications of exact structures and relative homological algebra to the study of invariants of multiparameter persistence modules. This paper is mostly expository, but does contain a pair of novel results. Over finite posets, classical ar
Externí odkaz:
http://arxiv.org/abs/2308.01790
Autor:
Hanson, Eric J.
We generalize the "facial weak order" of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its restriction t
Externí odkaz:
http://arxiv.org/abs/2305.06031
Autor:
Hanson, Eric J.
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 Bancroft's combinatorial model for the shard intersection order
Externí odkaz:
http://arxiv.org/abs/2303.11517
Autor:
Hanson, Eric J., You, Xinrui
Publikováno v:
Journal of Algebra 639 (2024), 464-497
The bricks over preprojective algebras of type A are known to be in bijection with certain combinatorial objects called "arcs". In this paper, we show how one can use arcs to compute bases for the Hom-spaces and first extension spaces between bricks.
Externí odkaz:
http://arxiv.org/abs/2303.11513
Autor:
Hanson, Eric J., Thomas, Hugh
Publikováno v:
Algebras and Representation Theory 27 (2024), 461-468
Recently, Buan and Marsh showed that if two complete $\tau$-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is $\tau$-tilting finite. They conjectured that the result holds without that a
Externí odkaz:
http://arxiv.org/abs/2302.07118