Recollement and Tilting Complexes

Abstract

First, we study recollement of a derived category of unbounded complexes of modules induced by a partial tilting complex. Second, we give equivalent conditions for P^centerdot to be a recollement tilting complex, that is, a tilting complex which induces an equivalence between recollements {D_A/AeA(A), D(A), D(eAe) and {D_B/BfB(B), D(B), D(fBf), where e, f are idempotents of A, B, respectively. In this case, there is an unbounded bimodule complex $\varDelta^{\centerdot}_{T}$ which induces an equivalence between D_A/AeA(A) and D_B/BfB(B). Third, we apply the above to a symmetric algebra A. We show that a partial tilting complex $P^{\centerdot}$