Loop groups and noncommutative geometry

Sebastiano Carpi, Robin Hillier
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;%%" }