On Serre dimension of finite dimensional algebras

It is known that a smooth projective variety is not always uniquely determined by its bounded derived category of coherent sheaves. Still the dimension of the variety is determined uniquely. Indeed, iterations of Serre functor on the derived category "move complexes to the left" with the speed equal to the dimension. This lead to the notion of "Serre dimension" of a good triangulated category. We discuss this notion focusing on derived categories of finite dimensional algebras.