The Lorentz group and its finite field analogues: local isomorphism and approximation
Mathematical Physics
2008-11-26 v2 math.MP
Abstract
Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real 4-dimensional space-time. Bounded subsets of the real Lorentz group are retractable with arbitrary accuracy to finite subsets of such rational subgroups. These finite retracts correspond, via local isomorphisms, to well-behaved subsets of Lorentz groups over finite fields. This establishes a relationship of approximation between the real Lorentz group and Lorentz groups over very large finite fields.
Keywords
Cite
@article{arxiv.0805.1224,
title = {The Lorentz group and its finite field analogues: local isomorphism and approximation},
author = {Stephan Foldes},
journal= {arXiv preprint arXiv:0805.1224},
year = {2008}
}