Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.17962 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- For a finite dimensional algebra $A$, the TF equivalence on the real Grothendieck group $K_0(\operatorname{\mathsf{proj}} A)_\mathbb{R}$ can be regarded as a completion of the $g$-fan. For example, the silting cones $C^\circ(U)$ of 2-term presilting complexes $U$ give the most fundamental family of TF equivalence classes. The next step is studying the TF equivalence classes around each silting cone $C^\circ(U)$. Thus, in this paper, we investigate the closed interval neighborhood $D(U)$ of $C^\circ(U)$. As our main result, we give a $2^{|U|}:1$ correspondence between the TF equivalence classes in $D(U)$ and those in $K_0(\operatorname{\mathsf{proj}} B)_\mathbb{R}$, where $B$ is the algebra appearing in the $τ$-tilting reduction at $U$. For this purpose, we give an explicit description of defining inequalities and the faces of $D(U)$ as a polyhedral cone, by using 2-term simple-minded collections and $M$-TF equivalences.