# Loop groups and noncommutative geometry

September 09, 2015

We describe the representation theory of loop groups in terms of K-theory and
noncommutative geometry. This is done by constructing suitable spectral triples
associated with the level l projective unitary positive-energy representations
of any given loop group LG. The construction is based on certain supersymmetric
conformal field theory models associated with LG.

open access link
Reviews in Mathemayical Physics 29, 1750029 (2017) [42 pages]

@article{Carpi:2015iya,
author = "Carpi, Sebastiano and Hillier, Robin",
title = "{Loop groups and noncommutative geometry}",
journal = "Rev. Math. Phys.",
volume = "29",
year = "2017",
number = "09",
pages = "1750029",
doi = "10.1142/S0129055X17500295",
note = "[APS Physics29,1750029(2017)]",
eprint = "1509.02509",
archivePrefix = "arXiv",
primaryClass = "math.OA",
SLACcitation = "%%CITATION = ARXIV:1509.02509;%%"
}

Keywords:

*none*