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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