Classification of Simple Weight Modules over the Schrödinger Algebra. Issue 1 (1st March 2018) - Bavula, V. V.; Lu, T.
Abstract: A classification of simple weight modules over the Schrödinger algebra is given. The Krull and the global dimensions are found for the centralizer ${C_{S}}(H)$ (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 ${C_{S}}(H)$ -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 ${C_{S}}(H)$ are tensor homological $/$ Krull minimal.