Alexander Schenkel

Title: Mapping spaces and automorphisms groups of toric NC spaces [pdf]
Abstract: A generic feature of NC geometry is that a deformed space has typically fewer automorphisms than its classical limit. Using techniques from sheaf topos theory, I show how to define internal automorphism groups of toric NC spaces (e.g. the Connes-Landi sphere), which are considerably `bigger' than the naive automorphism groups. These automorphism groups are generalized toric NC spaces and, using synthetic geometry techniques, one can define their Lie algebras, which I will identify with the braided derivations of the function algebras of the underlying toric NC spaces. As an application, I define the gauge group of a NC principal bundle (i.e. Hopf-Galois extension) and compute its Lie algebra. This talk is based on work in progress with G. E. Barnes and R. J. Szabo.