Gravity on Finite Groups

TL;DR

This paper develops a gravity-like field theory on finite groups, especially focusing on the nonabelian group S_3, by reviewing differential calculi and introducing new developments in the mathematical framework.

Contribution

It introduces a novel approach to formulating gravity-like theories on finite groups, with detailed analysis of differential calculus on S_3 and new theoretical insights.

Findings

Constructed a gravity-like field theory on S_3

Reviewed and extended differential calculus on finite groups

Provided detailed example of bicovariant calculus on S_3

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.