Some equivariant constructions in noncommutative algebraic geometry

Abstract

We here present rudiments of an approach to geometric actions in noncommutative algebraic geometry, based on geometrically admissible actions of monoidal categories. This generalizes the usual (co)module algebras over Hopf algebras which provide affine examples. We introduce a compatibility of monoidal actions and localizations which is a distributive law. There are satisfactory notions of equivariant objects, noncommutative fiber bundles and quotients in this setup.

20 pages, surveys basics of my long term project; v2: major revision in all parts; last section on search for Leibniz groups has been omitted, but its improved version can be found on my webpage at http://www.irb.hr/korisnici/zskoda/leibnizManifesto.pdf

References in corpus (7)

• Notes on Grothendieck topologies, fibered categories and descent theory
• Unoriented WZW Models and Holonomy of Bundle Gerbes
• Distributive laws for actions of monoidal categories
• Noncommutative geometry through monoidal categories
• Equivariant monads and equivariant lifts versus a 2-category of distributive laws
• Compatibility of (co)actions and localizations
• Bicategory of entwinings