Affinoid enveloping algebras and their representations
<p>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 alg...
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| Format: | Thesis |
| Language: | English |
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2020
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| _version_ | 1817933142627975168 |
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| author | Stanciu, I |
| author2 | Ardakov, K |
| author_facet | Ardakov, K Stanciu, I |
| author_sort | Stanciu, I |
| collection | OXFORD |
| description | <p>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.</p>
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| first_indexed | 2024-03-06T22:09:26Z |
| format | Thesis |
| id | oxford-uuid:514c1cbb-1f39-4c99-b908-9a2662878ae8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:49:07Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | oxford-uuid:514c1cbb-1f39-4c99-b908-9a2662878ae82024-12-08T12:18:35ZAffinoid enveloping algebras and their representationsThesishttp://purl.org/coar/resource_type/c_db06uuid:514c1cbb-1f39-4c99-b908-9a2662878ae8AlgebraMathematicsEnglishHyrax Deposit2020Stanciu, IArdakov, K<p>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.</p> |
| spellingShingle | Algebra Mathematics Stanciu, I Affinoid enveloping algebras and their representations |
| title | Affinoid enveloping algebras and their representations |
| title_full | Affinoid enveloping algebras and their representations |
| title_fullStr | Affinoid enveloping algebras and their representations |
| title_full_unstemmed | Affinoid enveloping algebras and their representations |
| title_short | Affinoid enveloping algebras and their representations |
| title_sort | affinoid enveloping algebras and their representations |
| topic | Algebra Mathematics |
| work_keys_str_mv | AT stanciui affinoidenvelopingalgebrasandtheirrepresentations |