Gravity on Finite Groups

Abstract

Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group S_3 is treated in detail, and used to build a gravity-like field theory on S_3.

LaTeX, 26 pages, 1 figure. Corrected misprints and formula giving exterior product of n 1-forms. Added note on topological action

Cited by in corpus (8)

• Noncommutative geometry and physics: a review of selected recent results
• Riemannian geometry of quantum groups and finite groups with nonuniversal differentials
• Electromagnetism and Gauge Theory on the Permutation Group $S_3$
• Differential Geometry of Group Lattices
• Discretized Yang-Mills and Born-Infeld actions on finite group geometries
• Finite group discretization of Yang-Mills and Einstein actions
• Riemannian Geometry of Bicovariant Group Lattices
• Noncommutative de Rham cohomology of finite groups