paper

Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms

arXiv:1409.6331 · doi:10.1016/j.geomphys.2014.12.005

Abstract

We 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.

arXiv commentv1: 56 pages. v2: 57 pages. Introduction expanded. Published in Journal of Geometry and Physics

References in corpus (25)

Cited by in corpus (26)