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Canonical connections

Chuang, Ken-Hsien (2014) Canonical connections. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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We study the space of canonical connections on a reductive homogeneous space. Through the investigation of lines in the space of connections invariant under parallelism, we prove that on a compact simple Lie group, bi-invariant canonical connections are exactly the bi-invariant connections that are invariant under parallelism. This motivates our definition of a family of canonical connections on Lie groups that generalizes the classical $(+)$, $(0)$, and $(-)$ connections studied by Cartan and Schouten. We find the horizontal lift equation of each connection in this family, as well as compute the square of the corresponding Dirac operator as the element of non-commutative Weil algebra defined by Alekseev and Meinrenken.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Chuang, Ken-Hsienkec39@pitt.eduKEC39
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairIon, Bogdanbion@pitt.eduBION
Committee MemberHales, Thomashales@pitt.eduHALES
Committee MemberSparling,
Committee MemberKrafty,
Date: 28 May 2014
Date Type: Publication
Defense Date: 25 February 2014
Approval Date: 28 May 2014
Submission Date: 10 April 2014
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 95
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: canonical connections, Cartan-Schouten connections, Dirac operators
Date Deposited: 28 May 2014 16:28
Last Modified: 15 Nov 2016 14:19


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