Extending tilting modules to one-point extensions by projectives

摘要

Let k be an algebraically closed field, B be a finite dimensional k-algebra and A be the one-point extension of B by the projective B-module P-0. We compare the posets T-A and T-B of tilting A-modules and B-modules, respectively. We prove that the restriction and the extension functors de. ne morphisms of posets r:T-A -> T-B and e:T-B -> T-A such that re = id. Moreover, e induces a full embedding of the quiver of T-B into that of T-A, whose image is closed under successors, and mapping distinct connected components of the first into distinct connected components of the second.