Classification of Simple Weight Modules over the Schrödinger Algebra. Issue 1 (1st March 2018)

• Record Type: Journal Article
• Authors: Bavula, V. V.; Lu, T.
• Is Part Of: Canadian mathematical bulletin =. Volume 61:Issue 1(2018)
• Page Start: 16
• Page End: 39
• Publication Date: 2018-03-01
• Subjects: 17B10 -- 17B20 -- 17B35 -- 16E10 -- 16P90 -- 16P40 -- 16P50; weight module -- simple module -- centralizer -- Krull dimension -- global dimension -- tensor homological minimal algebra -- tensor Krull minimal algebra; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2017-017-7
• Languages: English
• ISSNs: 0008-4395

Abstract

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.