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This is another question asking for references. There is an important phenomenon of correspondence between (complexes of) representations of infinite-dimensional Lie algebras with the complementary ...

is the following true (all algebras and modules are assumed to be finite dimensional): The finitistic dimension of an algebra is equal to the supremum of projective dimensions of tilting modules? It ...

The following is an open problem: Given a partial tilting module $T$ over a finite dimensional algebra $A$ (that is $Ext_A^i(T,T)=0$ for all $i \geq 1$ and $pd(T) < \infty$), then $T$ is a tilting ...