Journal article
Categorical tori
N Ganter
Symmetry Integrability and Geometry Methods and Applications Sigma | NATL ACAD SCI UKRAINE, INST MATH | Published : 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.
Related Projects (1)
Grants
Awarded by Appalachian Regional Commission
Funding Acknowledgements
The author was supported by an Australian Research Fellowship and by ARC grant DP1095815. It is a pleasure to thank David Roberts for very helpful conversations and correspondence as well as his open referee report. The idea for Construction 2.1 came from a conversation with him, and I understand that he will also write about it elsewhere. I would like to thank Shan Shah for pointing out a mistake in an earlier version. Many thanks for helpful and inspiring conversations also go to Matthew Ando, Konrad Waldorf, Thomas Nikolaus, Geoffrey Mason, Arun Ram, and Alex Ghitza. Finally I wish to thank the anonymous referee for helpful comments.