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Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces - 1st Edition - ISBN: 9780128117736, 9780128117743

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

1st Edition

Author: Abraham Ungar
Paperback ISBN: 9780128117736
eBook ISBN: 9780128117743
Imprint: Academic Press
Published Date: 4th January 2018
Page Count: 418
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Table of Contents

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


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.

Key Features

  • Introduces the study of generalized gyrogroups and gyrovector spaces
  • Develops new algebraic structures, bi-gyrogroups and bi-gyrovector spaces
  • Helps readers to surmount boundaries between algebra, geometry and physics
  • Assists readers to parametrize and describe the full set of generalized Lorentz transformations in a geometric way
  • Generalizes approaches from gyrogroups and gyrovector spaces to bi-gyrogroups and bi-gyrovector spaces with geometric entanglement


Graduate students and exceptional undergraduate students and 1st year PhDs in hyperbolic and differential geometry, linear algebra, group theory and loop theory, and mathematical physicists


No. of pages:
© Academic Press 2018
4th January 2018
Academic Press
Paperback ISBN:
eBook ISBN:


"This monograph is a synthesis of the author’s work on gyrogroups and gyrovector spaces (since 1988) as well as on their generalizations, the bi-gyrogroups and bi-gyrovector spaces. ...This very original but highly technical book starts with an interesting modelization of the Einstein addition of the velocities in the relativistic setting, by considering it as the (nonassociative) composition law of a special groupoid, called gyrogroup." --zbMATh

Ratings and Reviews

About the Author

Abraham Ungar

Abraham Ungar (North Dakota State University, ND) is Professor of Mathematics at North Dakota State University. He specializes in the areas of linear algebra, geometry and physics. He has published seven books and over 100 papers, mostly in indexed journals.

Affiliations and Expertise

Professor of Mathematics at North Dakota State University