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Classification of Simple Weight Modules over the Schrödinger Algebra
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- Journal:
- Canadian Mathematical Bulletin / Volume 61 / Issue 1 / 01 March 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 16-39
- Print publication:
- 01 March 2018
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- Article
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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.
