Abstract
The four gyrocommutative gyrogroups that we explore in this book,
-
(1)
the real Einstein gyrogroup of relativistically admissible velocities;
-
(2)
the complex Einstein gyrogroup;
-
(3)
the Ungar gyrogroup of relativistically proper velocities; and
-
(4)
the Möbius gyrogroup
are briefly reviewed. Following the observation that each of these possesses a cocycle form, we we will explore in this chapter the cocycle forms in abstract gyrocommutative gyrogroups. These will prove useful in the study of various Lorentz groups that result from the extension of various gyrocommutative gyrogroups with cocycle forms.
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© 2001 Kluwer Academic Publishers
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Ungar, A.A. (2001). The Cocycle Form. In: Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession. Fundamental Theories of Physics, vol 117. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9122-0_9
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DOI: https://doi.org/10.1007/978-94-010-9122-0_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6910-3
Online ISBN: 978-94-010-9122-0
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