l'Innocente, Sonia and Prest, Mike
(2006)
*Rings of definable scalars of Verma modules.*
[MIMS Preprint]

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## Abstract

Let M be a Verma module over the Lie algebra, sl2(k), of trace zero 2×2 matrices over the algebraically closed field k. We show that the ring, RM, of definable scalars of M is a von Neumann regular ring and that the canonical map from U(sl2(k)) to RM is an epimorphism of rings. We also describe the Ziegler closure of M. The proofs make use of ideas from the model theory of modules.

Item Type: | MIMS Preprint |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras |

Depositing User: | Professor Mike Prest |

Date Deposited: | 22 May 2006 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/277 |

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