Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

1st Edition - January 4, 2018

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  • Author: Abraham Ungar
  • Paperback ISBN: 9780128117736
  • eBook ISBN: 9780128117743

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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

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)

Product details

  • No. of pages: 418
  • Language: English
  • Copyright: © Academic Press 2018
  • Published: January 4, 2018
  • Imprint: Academic Press
  • Paperback ISBN: 9780128117736
  • eBook ISBN: 9780128117743

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

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