Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
140 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the Enlargement by Prüfer Objects of the Cluster Category of type $A_\infty$ (1411.4856v3)

Published 18 Nov 2014 in math.RT

Abstract: In a paper by Holm and Jorgensen, the cluster category $\mathscr{D}$ of type $A_\infty$, with Auslander-Reiten quiver $\mathbb{Z} A_\infty$, is introduced. Slices in the Auslander-Reiten quiver of $\mathscr{D}$ give rise to direct systems; the homotopy colimit of such direct systems can be computed and these "Pr\"ufer objects" can be adjoined to form a larger category. It is this larger category, $\overline{\mathscr{D}},$ which is the main object of study in this paper. We show that $\overline{\mathscr{D}}$ inherits a nice geometrical structure from $\mathscr{D}$; "arcs" between non-neighbouring integers on the number line correspond to indecomposable objects, and in the case of $\overline{\mathscr{D}}$ we also have arcs to infinity which correspond to the Pr\"ufer objects. During the course of this paper, we show that $\overline{\mathscr{D}}$ is triangulated, compute homs, investigate the geometric model, and we conclude by computing the cluster tilting subcategories of $\overline{\mathscr{D}}$.

Summary

We haven't generated a summary for this paper yet.