Details

Autor(en) / Beteiligte

• Evans, David E.
• Gannon, Terry

Titel

Tambara-Yamagami, loop groups, bundles and KK-theory

Ist Teil von

• Advances in mathematics (New York. 1965), 2023-05, Vol.421, p.109002, Article 109002

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• This paper is part of a sequence interpreting quantities of conformal field theories K-theoretically. Here we give geometric constructions of the associated module categories (modular invariants, nimreps, etc). In particular, we give a KK-theory interpretation of all modular invariants for the loop groups of tori, as well as most known modular invariants of loop groups. In addition, we find unexpectedly that the Tambara-Yamagami fusion category has an elegant description as bundles over a groupoid, and use that to interpret its module categories as KK-elements. We establish reconstruction for the doubles of all Tambara-Yamagami categories, generalising work of Bischoff to even-order groups. We conclude by relating the modular group representations coming from finite groups and loop groups to the Chern character and to the Fourier-Mukai transform respectively.