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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…
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…
Algebraic deformations of toric varieties I. General constructions
Lucio Cirio, Giovanni Landi, Richard J. Szabo
We construct and study noncommutative deformations of toric varieties by combining techniques from toric geometry, isospectral deformations, and noncommutative geometry in braided…