Academic Press Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces (Mathematical Analysis and its Applications)

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. Review "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 Review This research monograph provides a novel, elegant and important parametric conceptualization of pseudo-rotations that crosses boundaries between algebra, geometry and physics From the Back Cover 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 Einsteins 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 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 pseudo Lorentz transformations in a geometric way Generalizes approaches from gyrogroups to bi-gyrogroups About the Author Abraham Ungar is Professor of Mathematics at North Dakota State University in North Dakota. He specializes in the areas of linear algebra, geometry, and physics. He has published seven books and over 100 papers, mostly in indexed journals. About Mathematics in Science and Engineering Series Editor: Themistocles Rassias Editorial Board: Sever Dragomir, Soon-Mo Jung, Gradimir Milovanovic, Hari Srivastava This new series of highly specialized research monographs, introductory handbooks and selected multi-contributor reference works (edited volumes), seeks to address developments in global analysis, non-linear analysis and the many problems of associated fields, including dynamical systems, ergodic theory, combinatorics, differential equations, approximation theory, analytic inequalities, functional equations, probability theory. The series comprises highly specialized research monographs written by eminent scientists, handbooks and selected multi-contributor reference works (edited volumes), bringing together an extensive body of information. This series presents pertinent interdisciplinary research progress in a variety of subject areas with Mathematical Analysis as a basis, addressing developments in global analysis, non-linear analysis and the many problems of associated fields, including dynamical systems, ergodic theory, combinatorics, differential equations, approximation theory, analytic inequalities, functional equations, and probability theory. The series deals with the fundamental interplay of nonlinear analysis with other headline domains (particularly geometry and analytic number theory) within the mathematical sciences. About the Author