Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphismsTools Barnes, Gwendolyn E., Schenkel, Alexander and Szabo, Richard J. (2015) Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphisms. Journal of Geometry and Physics, 89 . pp. 111-152. ISSN 0393-0440 Full text not available from this repository.
Official URL: https://doi.org/10.1016/j.geomphys.2014.12.005
AbstractWe systematically study noncommutative and nonassociative algebras A and their bimodules as algebras and bimodules internal to the representation category of a quasitriangular quasi-Hopf algebra. We enlarge the morphisms of the monoidal category of A-bimodules by internal homomorphisms, and describe explicitly their evaluation and composition morphisms. For braided commutative algebras A the full subcategory of symmetric A-bimodule objects is a braided closed monoidal category, from which we obtain an internal tensor product operation on internal homomorphisms. We describe how these structures deform under cochain twisting of the quasi-Hopf algebra, and apply the formalism to the example of deformation quantization of equivariant vector bundles over a smooth manifold. Our constructions set up the basic ingredients for the systematic development of differential geometry internal to the quasi-Hopf representation category, which will be tackled in the sequels to this paper, together with applications to models of noncommutative and nonassociative gravity such as those anticipated from non-geometric string theory.
Actions (Archive Staff Only)
|
Tools
Tools
