Loop groups and noncommutative geometry

Carpi, Sebastiano and Hillier, Robin Oliver (2017) Loop groups and noncommutative geometry. Reviews in Mathematical Physics, 29 (9): 1750029. ISSN 0129-055X

[thumbnail of LoopGroupNCG_RMP_Revised2_170816]
PDF (LoopGroupNCG_RMP_Revised2_170816)
LoopGroupNCG_RMP_Revised2_170816.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (604kB)


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 ℓℓ projective unitary positive-energy representations of any given loop group LGLG. The construction is based on certain supersymmetric conformal field theory models associated with LGLG in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.

Item Type:
Journal Article
Journal or Publication Title:
Reviews in Mathematical Physics
Additional Information:
Electronic version of this article published as Loop groups and noncommutative geometry Sebastiano Carpi and Robin Hillier Reviews in Mathematical Physics 2017 29:09 in Reviews in Mathematical Physics, 29, 9, 2017, 42 Pages] 10.1142/S0129055X17500295 ©2017 World Scientific Publishing Company http://www.worldscientific.com/worldscinet/rmp
Uncontrolled Keywords:
?? conformal netsfusion ringspectral triplesjlo cocyclesk-theorymathematical physicsstatistical and nonlinear physics ??
ID Code:
Deposited By:
Deposited On:
22 Aug 2017 13:34
Last Modified:
26 Jan 2024 01:20