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Title: Central extensions of Current Groups and the Jacobi Group
Author: Docherty, Pamela Jane
ISNI:       0000 0004 2746 3275
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2012
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A current group GX is an infinite-dimensional Lie group of smooth maps from a smooth manifold X to a finite-dimensional Lie group G, endowed with pointwise multiplication. This thesis concerns current groups G§ for compact Riemann surfaces §. We extend some results in the literature to discuss the topology of G§ where G has non-trivial fundamental group, and use these results to discuss the theory of central extensions of G§. The second object of interest in the thesis is the Jacobi group, which we think of as being associated to a compact Riemann surface of genus one. A connection is made between the Jacobi group and a certain central extension of G§. Finally, we define a generalisation of the Jacobi group that may be thought of as being associated to a compact Riemann surface of genus g ≥ 1.
Supervisor: Braden, Harry; Gordon, Iain Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: central extensions ; current groups ; Jacobi