Classification of Simple Weight Modules over the Schrodinger Algebra

Abstract

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.

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Authors/Creators:	Bavula, VV. Lu, T.
Copyright, Publisher and Additional Information:	© 2018 Canadian Mathematical Society. This is an author produced version of a paper subsequently published in Canadian Mathematical Bulletin. Uploaded in accordance with the publisher's self-archiving policy.
Keywords:	weight module; simple module; centralizer; Krull dimension; global dimension; tensor homological minimal algebra; tensor Krull minimal algebra
Dates:	Published (online): 23 May 2017 Published: March 2018
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User:	Symplectic Sheffield
Date Deposited:	19 Jun 2018 12:16
Last Modified:	25 Jun 2023 21:23
Published Version:	https://doi.org/10.4153/CMB-2017-017-7
Status:	Published
Publisher:	Canadian Mathematical Society
Refereed:	Yes
Identification Number:	https://doi.org/10.4153/CMB-2017-017-7
Related URLs:	Author

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Classification of Simple Weight Modules over the Schrodinger Algebra

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