Classification of Simple Weight Modules over the Schrodinger Algebra

A classification of simple weight modules over the Schrödinger algebra is given. The Krull and the global dimensions are found for the centralizer CS(H) (and some of its prime factor algebras) of the Cartan element H in the universal enveloping algebra S of the Schrödinger (Lie) algebra. The simple CS(H)-modules are classified. The Krull and the global dimensions are found for some (prime) factor algebras of the algebra S (over the centre). It is proved that some (prime) factor algebras of S and CS(H) are tensor homological/Krull minimal.