Affinoid enveloping algebras and their representations

Thesis

We develop the basic theory of Picard algebroids and twisted differential operators on a smooth, reduced, locally of finite type scheme over a commutative ring. We also give a new geometric proof of the classical Duflo's theorem. We next move to the study the affinoid enveloping algebra of a semisimple Lie algebra defined over a discrete valuation ring. We prove that there exists a one-to-one correspondence between the lattice of submodules of an affinoid Verma module of a given weight and the corresponding classical Verma module. Finally, we classify all the primitive ideals in the affinoid enveloping algebra and prove that a large class of two-sided ideals in the affinoid enveloping algebra is controlled by two-sided ideals in the classical enveloping algebra.

Authors: Stanciu, I

• DOI: 10.5287/ora-4jmj2enp9
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Non-commutative rings; D-modules; p-adic representation theory; Lie Algebras
• Subjects: Algebra; Mathematics