60 citations · 722 across the 62 of their papers we have counts for
8 papers · 1 filter
Dirac operators on noncommutative hypersurfaces
Hans Nguyen, Alexander Schenkel
This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce di…
On the Relationship between Classical and Deformed Hopf Fibrations
Tomasz Brzeziński, James Gaunt, Alexander Schenkel
The -deformed Hopf fibration over the commutative -sphere is compared with its classical counterpart. It is shown that there exists a natural…
Mapping spaces and automorphism groups of toric noncommutative spaces
Gwendolyn E. Barnes, Alexander Schenkel, Richard J. Szabo
We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an applic…
Noncommutative principal bundles through twist deformation
Paolo Aschieri, Pierre Bieliavsky, Chiara Pagani +1
We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a defo…
Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
Gwendolyn E. Barnes, Alexander Schenkel, Richard J. Szabo
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. W…
Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
Gwendolyn E. Barnes, Alexander Schenkel, Richard J. Szabo
We systematically study noncommutative and nonassociative algebras A and their bimodules as algebras and bimodules internal to the representation category of a quasitriangular quas…