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  • LoopGroupNCG_RMP_Revised2_170816

    Rights statement: 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

    Accepted author manuscript, 590 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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Loop groups and noncommutative geometry

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Loop groups and noncommutative geometry. / Carpi, Sebastiano; Hillier, Robin Oliver.

In: Reviews in Mathematical Physics, Vol. 29, No. 9, 1750029, 10.2017.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Carpi, S & Hillier, RO 2017, 'Loop groups and noncommutative geometry', Reviews in Mathematical Physics, vol. 29, no. 9, 1750029. https://doi.org/10.1142/S0129055X17500295

APA

Carpi, S., & Hillier, R. O. (2017). Loop groups and noncommutative geometry. Reviews in Mathematical Physics, 29(9), [1750029]. https://doi.org/10.1142/S0129055X17500295

Vancouver

Carpi S, Hillier RO. Loop groups and noncommutative geometry. Reviews in Mathematical Physics. 2017 Oct;29(9):1750029. Epub 2017 Sep 1. doi: 10.1142/S0129055X17500295

Author

Carpi, Sebastiano ; Hillier, Robin Oliver. / Loop groups and noncommutative geometry. In: Reviews in Mathematical Physics. 2017 ; Vol. 29, No. 9.

Bibtex

@article{cc849459704840c69570f3ba57b36236,
title = "Loop groups and noncommutative geometry",
abstract = "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.",
keywords = "Conformal nets, fusion ring, spectral triples, JLO cocycles, K-theory",
author = "Sebastiano Carpi and Hillier, {Robin Oliver}",
note = "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 {\textcopyright}2017 World Scientific Publishing Company http://www.worldscientific.com/worldscinet/rmp",
year = "2017",
month = oct,
doi = "10.1142/S0129055X17500295",
language = "English",
volume = "29",
journal = "Reviews in Mathematical Physics",
issn = "0129-055X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "9",

}

RIS

TY - JOUR

T1 - Loop groups and noncommutative geometry

AU - Carpi, Sebastiano

AU - Hillier, Robin Oliver

N1 - 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

PY - 2017/10

Y1 - 2017/10

N2 - 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.

AB - 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.

KW - Conformal nets

KW - fusion ring

KW - spectral triples

KW - JLO cocycles

KW - K-theory

U2 - 10.1142/S0129055X17500295

DO - 10.1142/S0129055X17500295

M3 - Journal article

VL - 29

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 9

M1 - 1750029

ER -