Results 31 to 40 of about 2,140 (101)
On the Auslander-Reiten Quiver of the Representations of an Infinite Quiver [PDF]
Algebras and Representation Theory, 2012 Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. The main purpose of this paper is to get a better understanding of rep(Q) by means of its Auslander-Reiten quiver. To achieve this goal, we define a category C(Q) which is a full, abelian and Hom-finite
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Torsion classes of extended Dynkin quivers over commutative rings
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract For a Noetherian R$R$‐algebra Λ$\Lambda$, there is a canonical inclusion torsΛ→∏p∈SpecRtors(κ(p)Λ)$\mathop {\mathsf {tors}}\Lambda \rightarrow \prod _{\mathfrak {p}\in \operatorname{Spec}R}\mathop {\mathsf {tors}}(\kappa (\mathfrak {p})\Lambda)$, and each element in the image satisfies a certain compatibility condition.
Osamu Iyama, Yuta Kimura
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Cluster categories, m-cluster categories and diagonals in polygons [PDF]
, 2009 The goals of this expository article are on one hand to describe how to construct ($m$-) cluster categories from triangulations (resp. from $m+2$-angulations) of polygons.
Baur, Karin
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, 2019 These notes are an expanded version of my talk at the ICRA 2018 in Prague, Czech Republic; they are based on joint work with Tobias Dyckerhoff and Tashi Walde.
Jasso, Gustavo
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The shift‐homological spectrum and parametrising kernels of rank functions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift‐homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical.
Isaac Bird +2 more
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Remarks on τ$\tau$‐tilted versions of the second Brauer–Thrall conjecture
Bulletin of the London Mathematical Society, Volume 57, Issue 5, Page 1568-1583, May 2025.Abstract In this short note, we state a stable and a τ$\tau$‐reduced version of the second Brauer–Thrall conjecture. The former is a slight strengthening of a brick version of the second Brauer–Thrall conjecture raised by Mousavand and Schroll–Treffinger–Valdivieso.
Calvin Pfeifer
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Algebras of acyclic cluster type: tree type and type $\widetilde{A}$
, 2012 In this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of type $\widetilde{A}$.
Amiot +6 more
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Nakajima quiver varieties, affine crystals and combinatorics of Auslander-Reiten quivers
Algebra and Discrete Mathematics, 2022 We obtain an explicit crystal isomorphism between two realizations of crystal bases of finite dimensional irreducible representations of simple Lie algebras of type A and D. The first realization we consider is a geometric construction in terms of irreducible components of certain Nakajima quiver varieties established by Saito and the second is a ...
Kus, D., Schumann, B.
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Shift orbits for elementary representations of Kronecker quivers
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Let r∈N⩾3$r \in \mathbb {N}_{\geqslant 3}$. We denote by Kr$K_r$ the wild r$r$‐Kronecker quiver with r$r$ arrows γi:1⟶2$\gamma _i \colon 1 \longrightarrow 2$ and consider the action of the group Gr⊆Aut(Z2)$G_r \subseteq \operatorname{Aut}(\mathbb {Z}^2)$ generated by δ:Z2⟶Z2,(x,y)↦(y,x)$\delta \colon \mathbb {Z}^2 \longrightarrow \mathbb {Z}^2,
Daniel Bissinger
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The category of a partitioned fan
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract In this paper the notion of an admissible partition of a simplicial polyhedral fan is introduced and the category of a partitioned fan is defined as a generalisation of the τ$\tau$‐cluster morphism category of a finite‐dimensional algebra. This establishes a complete lattice of categories around the τ$\tau$‐cluster morphism category, which is ...
Maximilian Kaipel
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