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, R_M, of definable scalars of M is a von Neumann regular ring and that the canonical map from U(sl2(k)) to R_M 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.
Rings of definable scalars of Verma modules
L'INNOCENTE, Sonia;
2007-01-01
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, R_M, of definable scalars of M is a von Neumann regular ring and that the canonical map from U(sl2(k)) to R_M 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.File in questo prodotto:
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