The Lorentz group and its finite field analogues: local isomorphism and approximation

Details The Lorentz group and its finite field analogues: local isomorphism and approximation The Lorentz group and its finite field analogues: local isomorphism and approximation

2008-05-08

arxiv.org/abs/0805.1224v2

J.Math.Phys.49:093512,2008

Physics

Mathematical Physics

Scientific paper

10.1063/1.2982519

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.

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