ERA

Download the full-sized PDF of Representations of affine truncations of representation involutive-semirings of Lie algebras and root systems of higher typeDownload the full-sized PDF

Analytics

Share

Permanent link (DOI): https://doi.org/10.7939/R3D946

Download

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Graduate Studies and Research, Faculty of

Collections

This file is in the following collections:

Theses and Dissertations

Representations of affine truncations of representation involutive-semirings of Lie algebras and root systems of higher type Open Access

Descriptions

Other title
Subject/Keyword
Semirings (Mathematics)
Root systems (Algebra)
Lie algebras
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Graves, Timothy W
Supervisor and department
Gannon, Terry (Mathematical and Statistical Sciences)
Examining committee member and department
Czarnecki, Andrei (Physics)
Cliff, Gerald (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2011-04-14T18:36:43Z
Graduation date
2011-06
Degree
Master of Science
Degree level
Master's
Abstract
An important component of a rational conformal field theory is a representation of a certain involutive-semiring. In the case of Wess-Zumino-Witten models, the involutive-semiring is an affine truncation of the representation involutive-semiring of a finite-dimensional semisimple Lie algebra. We show how root systems naturally correspond to representations of an affine truncation of the representation involutive-semiring of sl_2(C). By reversing this procedure, one can, to a representation of an affine truncation of the representation involutive-semiring of an arbitrary finite-dimensional semisimple Lie algebra, associate a root system and a Cartan matrix of higher type. We show how this same procedure applies to a special subclass of representations of the nontruncated representation involutive-semiring, leading to higher-type analogues of the affine Cartan matrices. Finally, we extend the known results for sl_3(C) with a symmetric classification, a construction, and a list of computer-generated examples.
Language
English
DOI
doi:10.7939/R3D946
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication

File Details

Date Uploaded
Date Modified
2014-05-01T00:23:18.995+00:00
Audit Status
Audits have not yet been run on this file.
Characterization
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 997560
Last modified: 2015:10:12 13:12:48-06:00
Filename: Graves_Timothy_Spring 2011.pdf
Original checksum: 360bbb918e9e9c4f0a811b19eed41eeb
Well formed: true
Valid: true
Status message: Too many fonts to report; some fonts omitted. Total fonts = 1481
File title: Thesis.dvi
Page count: 198
Activity of users you follow
User Activity Date