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Quantum spaces arising from weighted circle actions and their non-commutative geometry. / Simon A Fairfax

Swansea University Author: Simon A Fairfax

Abstract

Introduction The purpose of this thesis is to investigate weighted actions of the circle group U(1) on known quantum spaces. By introducing suitable weights we are able to construct new unexplored quantum spaces which contain the known quantum spaces in the unweighted case. Once we are able to descr...

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Published: 2013
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42457
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first_indexed 2018-08-02T18:54:45Z
last_indexed 2018-08-03T10:10:12Z
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spelling 2018-08-02T16:24:29.3221945 v2 42457 2018-08-02 Quantum spaces arising from weighted circle actions and their non-commutative geometry. ab9d5a8e453b43a0e1587ecfaefa421e NULL Simon A Fairfax Simon A Fairfax true true 2018-08-02 Introduction The purpose of this thesis is to investigate weighted actions of the circle group U(1) on known quantum spaces. By introducing suitable weights we are able to construct new unexplored quantum spaces which contain the known quantum spaces in the unweighted case. Once we are able to describe the algebraic structure of these new quantum spaces we investigate their quantum geometry. This thesis is split into two main parts with an outlook of open problems attached; the first consists of introductory material, motivation and an overview of quantum groups and their non-commutative geometry. The second part contains the results from research into quantum weighted projective spaces, in particular describes quantum weighted projective spaces, quantum weighted real projective spaces and quantum weighted Heegaard spaces; see [5], [6] and [7]. Finally, some open problems are discusscd, firstly the existence of a differential calculus over the quantum weighted projective spaces. Secondly, the description of higher dimensional quantum weighted projective spaces. One possible approach for interpreting these spaces on the C*-algebra level is by graph algebra theory; the ideas are discussed briefly in the appendices of this thesis. (Abstract shortened by ProQuest.). E-Thesis Mathematics. 31 12 2013 2013-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:29.3221945 2018-08-02T16:24:29.3221945 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Simon A Fairfax NULL 1 0042457-02082018162455.pdf 10798165.pdf 2018-08-02T16:24:55.9370000 Output 4244221 application/pdf E-Thesis true 2018-08-02T16:24:55.9370000 false
title Quantum spaces arising from weighted circle actions and their non-commutative geometry.
spellingShingle Quantum spaces arising from weighted circle actions and their non-commutative geometry.
Simon A Fairfax
title_short Quantum spaces arising from weighted circle actions and their non-commutative geometry.
title_full Quantum spaces arising from weighted circle actions and their non-commutative geometry.
title_fullStr Quantum spaces arising from weighted circle actions and their non-commutative geometry.
title_full_unstemmed Quantum spaces arising from weighted circle actions and their non-commutative geometry.
title_sort Quantum spaces arising from weighted circle actions and their non-commutative geometry.
author_id_str_mv ab9d5a8e453b43a0e1587ecfaefa421e
author_id_fullname_str_mv ab9d5a8e453b43a0e1587ecfaefa421e_***_Simon A Fairfax
author Simon A Fairfax
author2 Simon A Fairfax
format E-Thesis
publishDate 2013
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description Introduction The purpose of this thesis is to investigate weighted actions of the circle group U(1) on known quantum spaces. By introducing suitable weights we are able to construct new unexplored quantum spaces which contain the known quantum spaces in the unweighted case. Once we are able to describe the algebraic structure of these new quantum spaces we investigate their quantum geometry. This thesis is split into two main parts with an outlook of open problems attached; the first consists of introductory material, motivation and an overview of quantum groups and their non-commutative geometry. The second part contains the results from research into quantum weighted projective spaces, in particular describes quantum weighted projective spaces, quantum weighted real projective spaces and quantum weighted Heegaard spaces; see [5], [6] and [7]. Finally, some open problems are discusscd, firstly the existence of a differential calculus over the quantum weighted projective spaces. Secondly, the description of higher dimensional quantum weighted projective spaces. One possible approach for interpreting these spaces on the C*-algebra level is by graph algebra theory; the ideas are discussed briefly in the appendices of this thesis. (Abstract shortened by ProQuest.).
published_date 2013-12-31T03:53:00Z
_version_ 1763752626616270848
score 11.035655

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