2024/12/23 by Ada Masters, Masters, Ada, Adam Rennie +1
Materials Science · Mathematics · #19K35 #46L87 #53C18 #58B32 #58B34 #Differential Geometry (math.DG) #Enzyme Structure and Function #FOS: Mathematics #History and Theory of Mathematics #K-Theory and Homology (math.KT) #Numerical methods for differential equations #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2412.17220
openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend unbounded Kasparov theory to encompass conformal group and quantum group equivariance. This new framework allows us to treat conformal actions on both manifolds and noncommutative spaces. As examples, we present unbounded representatives of Kasparov's γ-element for the real and complex Lorentz groups and display the conformal SLq(2)-equivariance of the standard spectral triple of the Podleś sphere. In pursuing descent for conformally equivariant cycles, we are led to a new framework for representing Kasparov classes. Our new representatives are unbounded, possess a dynamical quality, and also include known twisted spectral triples. We define an equivalence relation on these new representatives whose classes form an abelian group surjecting onto KK. The technical innovation which underpins these results is a novel multiplicative perturbation theory. By these means, we obtain Kasparov classes from the bounded transform with minimal side conditions.