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CLASSIFICATION OF
TRANSITIVE VERTEX ALGEBROIDS
by
Dmytro Chebotarov
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
August 2011
Copyright 2011 Dmytro Chebotarov
Object Description
| Title | Classification of transitive vertex algebroids |
| Author | Chebotarov, Dmytro |
| Author email | chebotar@usc.edu;chebotarov@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2011-05-23 |
| Date submitted | 2011-08-01 |
| Date approved | 2011-08-03 |
| Restricted until | 2011-08-03 |
| Date published | 2011-08-03 |
| Advisor (committee chair) | Malikov, Fedor |
| Advisor (committee member) |
Friedlander, Eric M. Pilch, Krzysztof |
| Abstract | In this dissertation we accomplish the following: ❧ 1) We present a classification of transitive vertex algebroids on a smooth variety X carried out in the spirit of Bressler's classification of Courant algebroids. In particular, we compute the class of the stack of transitive vertex algebroids. ❧ 2) We define deformations of sheaves of twisted chiral differential operators (TCDO) introduced in [AChM] and use the classification result to describe and classify such deformations. As a particular case, we obtain a localization of Wakimoto modules at non-critical level on flag manifolds. ❧ 3) We study representation theory of TCDO and their deformations. In particular, we show an equivalence between certain categories of modules over (deformed) TCDO and categories of twisted D-modules, thus extending a result of [AChM]. |
| Keyword | vertex algebras; algebroids; classification; representation theory |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Chebotarov, Dmytro |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume71/etd-Chebotarov-236-0.pdf |
Description
| Title | Page 1 |
| Full text | CLASSIFICATION OF TRANSITIVE VERTEX ALGEBROIDS by Dmytro Chebotarov A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) August 2011 Copyright 2011 Dmytro Chebotarov |
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