Folding quivers and numerical stability conditions. (arXiv:1210.0243v2 [math.RT] UPDATED)
We generalize Deng-Du's folding argument, for the bounded derived category
D(Q) of an acyclic quiver Q, to the finite dimensional derived category D(Gamma
Q) of the Ginzburg algebra Gamma Q associated to Q. We show that the F-stable
category of D(Gamma Q) is equivalent to the finite dimensional derived category
D(Gamma\SS) of the Ginzburg algebra Gamma\SS associated to the specie \SS,
which is folded from Q. Then we show that, if (Q,\SS) is of Dynkin type, the
principal component Stab_0 D(Gamma\SS) of the space of the stability conditions
of D(Gamma\SS) is canonically isomorphic to the principal component Stab_0^F
D(Gamma Q) of the space of F-stable stability conditions of D(Gamma Q). As an
application, we show that, if (Q,\SS) is of type (A_3, B_2) or (D_4, G_2), the
space Stab^N D(Gamma Q) of numerical stability conditions in Stab^0 D(Gamma Q),
consists of Br Gamma Q/Br Gamma\SS many connected components, each of which is
isomorphic to Stab^0 D(Gamma\SS) \cong Stab^F D(Gamma Q).查看全文