Discontinuous automorphisms of the proper Galilei and Euclidean groups

Journal Article · Sat Apr 01 04:00:00 EST 1989 · International Journal of Theoretical Physics; (USA)

DOI:https://doi.org/10.1007/BF00673297· OSTI ID:7165049

Adeleke, S A ^[1]

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1. Western Illinois Univ., Macomb (USA)

The author shows that there are numerous discontinuous automorphisms of the three-dimensional Euclidean group and thus of the Galilei group, as numerous as the subsets of the real numbers, 2{sup aleph-null}, to be exact. These automorphisms arise from the derivations of the field of real numbers. Tits gave an example of a discontinuous automorphism for the semidirect product of the general linear group GL{sub n}(K) in n dimensions with the additive group of n {times} n matrices. He observes that if one uses the quaternion representation of the rotations and the form of Tits example, one obtains discontinuous automorphisms of the Euclidean group in three dimensions. He shows that all automorphisms of the Euclidean group in higher dimensions are continuous.

• OSTI ID: 7165049
• Journal Information: International Journal of Theoretical Physics; (USA), Journal Name: International Journal of Theoretical Physics; (USA) Vol. 28:4; ISSN 0020-7748; ISSN IJTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EUCLIDEAN SPACE
GALILEI TRANSFORMATIONS
GROUP THEORY
INVARIANCE PRINCIPLES
MAPPING
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
MATHEMATICS
MOTION
RIEMANN SPACE
ROTATION
SPACE
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGICAL MAPPING
TOPOLOGY
TRANSFORMATIONS