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- Title
RINGS OF DEFINABLE SCALARS OF VERMA MODULES.
- Authors
L'INNOCENTE, SONIA; PREST, MIKE; Facchini, A.
- 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.
- Subjects
VERMA modules; MODULES (Algebra); LIE algebras; VON Neumann regular rings; RING extensions (Algebra); RING theory; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2007, Vol 6, Issue 5, p779
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498807002430