Abstract
For a finite-dimensional algebra A over a field K with n simple modules, the real Grothendieck group K0(projA)R:=K0(projA)⊗ZR≅Rn gives stability conditions of King. We study the associated wall-chamber structure of K0(projA)R by using the Koenig–Yang correspondences in silting theory. First, we introduce an equivalence relation on K0(projA)R called TF equivalence by using numerical torsion pairs of Baumann–Kamnitzer–Tingley. Second, we show that the open cone in K0(projA)R spanned by the g-vectors of each 2-term silting object gives a TF equivalence class, and this gives a one-to-one correspondence between the basic 2-term silting objects and the TF equivalence classes of full dimension. Finally, we determine the wall-chamber structure of K0(projA)R in the case that A is a path algebra of an acyclic quiver.
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