Year: 2025
Type: article
Abstract: Motivated by the Freed-Hopkins-Teleman theorem we study graded equivariant higher twists of K K -theory for the groups G = S U ( n ) G = SU(n) induced by exponential functors. We compute the rationalisation of these groups for all n n and all non-trivial functors. Classical twists use the determinant functor and yield equivariant bundles of compact operators that are classified by Dixmier-Douady theory. Their equivariant K K -theory reproduces the Verlinde ring of conformal field theory. Higher twists give equivariant bundles of stable uniformly hyperfinite algebras, which can be classified using stable homotopy theory. Rationally, only the K K -theory in degree dim ( G ) \dim (G) is again non-trivial. The non-vanishing group is a quotient of a localisation of the representation ring R ( G ) ⊗ Q R(G) \otimes \mathbb {Q} by a higher fusion ideal J F , Q J_{F,\mathbb {Q}} . We give generators for this ideal and prove that these can be obtained as derivatives of a potential. For the exterior algebra functor, which is exponential, we show that the determinant bundle over L S U ( n ) LSU(n) has a non-commutative counterpart where the fibre is the unitary group of the UHF algebra.
DOI: 10.1090/cams/60
Authors: David Evans, Ulrich Pennig
Institution: Cardiff University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: Leverhulme Trust
Award: G8055656002
OpenAlex ID: W4417329770