Tilting Modules
An A-module T is called a tilting module provided
- T has projective dimension at most 1.
- Ext1(T,T) = 0.
- The number of isomorphism classes of indecomposable direct summands of T is n(A).
If A is hereditary and T a tilting A-module, then B = End(T) is called a
tilted algebra.
Four classes of modules will be considered:
A
torsion pair (F,G) in mod A, and a torsion pair (Y,X)
in mod B, they are given by:
Examples:
- Progenerators are tilting modules.
- The BGP reflection functors (and more general, the APR-functors) are
of the form HomA(T,-),
with T a tilting module.