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Title: Primitive factor rings of p-adic completions of enveloping algebras as arithmetic differential operators
Author: Lewis, Benjamin
ISNI:       0000 0004 5370 2583
Awarding Body: Queen Mary, University of London
Current Institution: Queen Mary, University of London
Date of Award: 2015
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We study the -adic completion dD[1] of Berthelot's differential operators of level one on the projective line over a complete discrete valuation ring of mixed characteristic (0; p). The global sections are shown to be isomorphic to a Morita context whose objects are certain fractional ideals of primitive factor rings of the -adic completion of the universal enveloping algebra of sl2(R). We produce a bijection between the coadmissibly primitive ideals of the Arens Michael envelope of a nilpotent finite dimensional Lie algebra and the classical universal enveloping algebra. We make limited progress towards characterizing the primitive ideals of certain a noid enveloping algebras of nilpotent Lie algebras under restrictive conditions on the Lie algebra. We produce an isomorphism between the primitive factor rings of these affinoid enveloping algebras and matrix rings over certain deformations of Berthelot's arithmetic differential operators over the a fine line.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Algebra