Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 014, 18 pages      arXiv:1406.7046      https://doi.org/10.3842/SIGMA.2018.014
Contribution to the Special Issue on Moonshine and String Theory

Categorical Tori

Nora Ganter
School of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia

Received September 23, 2017, in final form January 31, 2018; Published online February 17, 2018

Abstract
We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal tori of simple and simply connected compact Lie groups and the tori associated to the Leech and Niemeyer lattices. We obtain the extraspecial 2-groups as the isomorphism classes of categorical fixed points under an involution action.

Key words: categorification; Lie group cohomology.

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