Tilting Theory: Elementary View

Often, tilting functors can be constructed very explicitly.

Example: We consider the following two algebras A and B.

As tilting A-module T we take the direct sum of the three A-modules P(1), P(3), τ-2P(1).

The functor F = Hom(T,-) is as follows:



Here, G is just the "hammock" for the simple module S(3).