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Group Extensions, Gerbes and Twisted K-theory
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2008 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis reviews the theory of group extensions, gerbes and twisted K-theory. Application to anomalies in gauge theory is briefly discussed. The main results are presented in two appended scientific papers. In the first paper we establish, by construction, a criterion for when an infinite dimensional abelian Lie algebra extension corresponds to a Lie group extension. In the second paper we introduce the fractional loop group L_qG, construct highest weight modules for the Lie algebra and discuss an application to twisted K-theory on G.

Place, publisher, year, edition, pages
Stockholm: KTH , 2008. , x, 48 p.
Series
Trita-FYS, ISSN 0280-316X ; 2008:7
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-4654ISBN: 978-91-7178-893-1 (print)OAI: oai:DiVA.org:kth-4654DiVA: diva2:13261
Presentation
2008-03-13, FA32, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101111Available from: 2008-02-27 Created: 2008-02-27 Last updated: 2010-11-11Bibliographically approved
List of papers
1. Integrability Criterion for Abelian Extensions of Lie Groups
Open this publication in new window or tab >>Integrability Criterion for Abelian Extensions of Lie Groups
2010 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 11, 4137-4148 p.Article in journal (Refereed) Published
Abstract [en]

We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras (g) over cap = g circle plus(omega) a integrates to a corresponding Lie group extension A (sic) (G) over cap (sic) G, where G is connected, simply connected and A congruent to a/Gamma for some discrete subgroup Gamma subset of a. When pi(1) (G) not equal 0, the kernel A is replaced by a central extension (A) over cap of pi(1) (G) by A.

Keyword
Infinite-dimensional Lie theory, abelian extensions
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-8043 (URN)10.1090/S0002-9939-2010-10423-9 (DOI)000284022300037 ()2-s2.0-78149258029 (Scopus ID)
Note
QC 20100915. Uppdaterad från accepted till published (20101213).Available from: 2008-02-27 Created: 2008-02-27 Last updated: 2017-12-14Bibliographically approved
2. Fractional Loop Group and Twisted K-theory
Open this publication in new window or tab >>Fractional Loop Group and Twisted K-theory
2010 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 299, no 3, 741-763 p.Article in journal (Refereed) Published
Abstract [en]

We study the structure of abelian extensions of the group L (q) G of q-differentiable loops (in the Sobolev sense), generalizing from the case of the central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are constructed for the Lie algebra. The construction is extended to the current algebra of the supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on G is discussed.

Keyword
unitary representations, quantization
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-8044 (URN)10.1007/s00220-010-1108-6 (DOI)000281711100007 ()2-s2.0-84755161215 (Scopus ID)
Note
QC 20100915 Uppdaterad från submitted till published (20101130).Available from: 2008-02-27 Created: 2008-02-27 Last updated: 2017-12-14Bibliographically approved

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Citation style
  • apa
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  • de-DE
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  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
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