The categorical automorphism group of the strict Lie 2-group classifying topological T-duality correspondences is a non-central categorical extension of the integral split pseudo-orthogonal group that splits over several subgroups and has 2-torsion k-invariant.
Categorical Tori
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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.
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Categorical symmetries of T-duality
The categorical automorphism group of the strict Lie 2-group classifying topological T-duality correspondences is a non-central categorical extension of the integral split pseudo-orthogonal group that splits over several subgroups and has 2-torsion k-invariant.