Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas.

Introduces the study of generalized gyrogroups and gyrovector spacesDevelops new algebraic structures, bi-gyrogroups and bi-gyrovector spacesHelps readers to surmount boundaries between algebra, geometry and physicsAssists readers to parametrize and describe the full set of generalized Lorentz transformations in a geometric wayGeneralizes approaches from gyrogroups and gyrovector spaces to bi-gyrogroups and bi-gyrovector spaces with geometric entanglement

1. Lorentz Transformations of signature (m,n) 2. Einstein Bi-gyrogroups of Order (m,n) 3. Einstein Bi-gyrovector Spaces of Order (m,n)