from the lorentz transformation group in pseudo-euclidean spaces to bi-gyrogroups
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abstract
the aim of this article is to extend the study of the lorentz transformation of order (m,n) from m=1 and n>=1 to all m,n>=1, obtaining algebraic structures called a bi-gyrogroup and a bi-gyrovector space. a bi-gyrogroup is a gyrogroup each gyration of which is a pair of a left gyration and a right gyration. a bi-gyrovector space is constructed from a bi-gyrocommutative bi-gyrogroup that admits a scalar multiplication.
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mathematics interdisciplinary researchجلد ۱، شماره ۱، صفحات ۲۲۹-۲۷۲
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