Zobrazeno 1 - 10
of 214
pro vyhledávání: '"Treffinger, P."'
Autor:
Tattar, Aran, Treffinger, Hipolito
In this paper we show an explicit relation between chains of torsion classes and weak stability conditions over an abelian category. In particular, up to a natural equivalence, they coincide. We investigate topological properties of the space of chai
Externí odkaz:
http://arxiv.org/abs/2306.08589
The wall-and-chamber structure is a geometric invariant that can be associated to any algebra. In this notes we give the definition of this object and we explain its relationship with torsion classes and $\tau$-tilting theory.
Comment: These are
Comment: These are
Externí odkaz:
http://arxiv.org/abs/2302.12699
We show how the $\tau$-cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that the category is well-defined.
Comment: 20 pages, 5 figures. Com
Comment: 20 pages, 5 figures. Com
Externí odkaz:
http://arxiv.org/abs/2302.12217
Autor:
August, Jenny, Haugland, Johanne, Jacobsen, Karin M., Kvamme, Sondre, Palu, Yann, Treffinger, Hipolito
Let $\mathcal{A}$ be an abelian length category containing a $d$-cluster tilting subcategory $\mathcal{M}$. We prove that a subcategory of $\mathcal{M}$ is a $d$-torsion class if and only if it is closed under $d$-extensions and $d$-quotients. This g
Externí odkaz:
http://arxiv.org/abs/2301.10463
Autor:
Schroll, Sibylle, Tattar, Aran, Treffinger, Hipolito, Valdivieso, Yadira, Williams, Nicholas J.
The stability space of a module is the cone of vectors which make the module semistable. These cones are defined in terms of inequalities; in this paper we draw insights from considering the dual description in terms of non-negative linear spans. We
Externí odkaz:
http://arxiv.org/abs/2208.15000
Let $B$ be a finite dimensional algebra and $A=B[P_0]$ be the one-point extension algebra of $B$ with respect to the finitely generated projective $B$-module $P_0$. The categories of $B$-modules and $A$-modules are related by two adjoint functors $\m
Externí odkaz:
http://arxiv.org/abs/2208.12703
The main theme of this paper is to study $\tau$-tilting subcategories in an abelian category $\mathscr{A}$ with enough projective objects. We introduce the notion of $\tau$-cotorsion torsion triples and show a bijection between the collection of $\ta
Externí odkaz:
http://arxiv.org/abs/2207.00457
In this paper we give a characterisation of trivial extension algebras in terms of quivers with relations. This result is based on a explicit description of the ideal of relations of the trivial extension of an algebra, given by the first author in t
Externí odkaz:
http://arxiv.org/abs/2206.04581
Categorification of scattering amplitudes for planar Feynman diagrams in scalar field theories with a polynomial potential is reported. Amplitudes for cubic theories are directly written down in terms of projectives of hearts of intermediate $t$-stru
Externí odkaz:
http://arxiv.org/abs/2112.14288
In this paper we study the Cartan matrix associated to the Ext-projective stratifying system induced by a basic and $\tau$-rigid object $M$ in mod$(A)$ by means of the $g$-vectors of the indecomposable direct summands of $M$. In particular we show th
Externí odkaz:
http://arxiv.org/abs/2111.11376