Abraham A. Ungar

North Dakota State University

[ 1 ] - Abraham A. Ungar's Autobiography

This autobiography presents the scientific living of Abraham Ungar and his role in Gyrogroups and Gyrovector spaces.‎

[ 2 ] - The Intrinsic Beauty, Harmony and Interdisciplinarity in Einstein Velocity Addition Law: Gyrogroups and Gyrovector Spaces

The only justification for the Einstein velocity addition law ‎appeared to be its empirical adequacy‎, ‎so that the ‎intrinsic beauty and harmony in Einstein addition remained for a long time ‎a mystery to be conquered‎. ‎Accordingly‎, ‎the aim of this expository article is to present ‎(i) the Einstein relativistic vector addition‎, ‎(ii) the resulting Einstein scalar multiplication‎, ‎(iii) th...

[ 3 ] - Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{...

[ 4 ] - From the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups

‎The Lorentz transformation of order $(m=1,n)$‎, ‎$ninNb$‎, ‎is the well-known ‎Lorentz transformation of special relativity theory‎. ‎It is a transformation of time-space coordinates of the ‎pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and ‎$n$ space dimensions ($n=3$ in physical applications)‎. ‎A Lorentz transformation without rotations is called a {it boost}‎. ‎Commonly‎, ‎the ...

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