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2006.90: Rings of definable scalars of Verma modules

2006.90: Sonia l'Innocente and Mike Prest (2006) Rings of definable scalars of Verma modules.

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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
Subjects:MSC 2000 > 03 Mathematical logic and foundations
MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 17 Nonassociative rings and algebras
MIMS number:2006.90
Deposited By:Professor Mike Prest
Deposited On:22 May 2006

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