Central extensions of Current Groups and the Jacobi Group
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Date
28/11/2012Author
Docherty, Pamela Jane
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Abstract
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.