The wall-chamber structures of the real Grothendieck groups
Sota Asai (Osaka University)
Abstract: For a given finite-dimensional algebra A over a field, stability conditions introduced by King define the wall-chamber structure of the real Grothendieck group K0(projA)R , as in the works of Br"{u}stle–Smith–Treffinger and Bridgeland. In this talk, I would like to explain my result that the chambers in this wall-chamber structure are precisely the open cones associated to the basic 2-term silting objects in the perfect derived category. As one of the key steps, I introduced an equivalence relation called TF equivalence by using numerical torsion pairs of Baumann–Kamnitzer–Tingley. If time permits, I will give some further results which were obtained in the ongoing joint work with Osamu Iyama.
Mathematics
Audience: researchers in the discipline
Series comments: The Workshop and International Conference on Representations of Algebras (ICRA) will take place online between 9th November and 25th November 2020.
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Deadline for submitting research snapshots: November 1st, 2020
| Organizers: | Lidia Angeleri Hügel, Aslak Bakke Buan, Gustavo Jasso*, Henning Krause, Rosanna Laking, Øyvind Solberg |
| *contact for this listing |