Chuang, Ken-Hsien
(2014)
Canonical connections.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
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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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| 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 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/21160 |
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