2015/05/09 by Abraham A. Ungar, Ungar, Abraham A.
Mathematics · #20N02 #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1505.02301
openalex publication_date 2015/05/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The Lorentz transformation group SO(m,n) is a group of Lorentz\ntransformations of order (m,n), that is, a group of special linear\ntransformations in a pseudo-Euclidean space of signature (m,n) that leave the\npseudo-Euclidean inner product invariant. A parametrization of SO(m,n) is\npresented, giving rise to the composition law of Lorentz transformations of\norder (m,n) in terms of parameter composition. The parameter composition, in\nturn, gives rise to a novel group-like structure called a bi-gyrogroup.\nBi-gyrogroups form a natural generalization of gyrogroups where the latter form\na natural generalization of groups. Like the abstract gyrogroup, the abstract\nbi-gyrogroup can play a universal computational role which extends far beyond\nthe domain of pseudo-Euclidean spaces.\n