Central extensions for loop groups of area-preserving diffeomorphisms and their fuzzy sphere limits
Mathematical Physics
2026-03-10 v1 Differential Geometry
math.MP
Abstract
We classify central extensions for the loop group LSDiff(S^2) of area-preserving diffeomorphisms of the 2-sphere, and of related twisted loop groups. We then show that the corresponding Lie algebra cocycles are `fuzzy sphere limits' of Kac-Moody cocycles for (twisted) loop algebras Lsu(k+1) for the limit of large k, provided that the cocycles are rescaled by 6/k^3.
Keywords
Cite
@article{arxiv.2603.06876,
title = {Central extensions for loop groups of area-preserving diffeomorphisms and their fuzzy sphere limits},
author = {Bas Janssens and Zhenghan Wang},
journal= {arXiv preprint arXiv:2603.06876},
year = {2026}
}
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39 pages