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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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
|Deposited By:||Professor Mike Prest|
|Deposited On:||22 May 2006|