عنوان
پدید آورنده
موضوع
رده
QC173.65
QC173
.
65
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
0128117745
(Number (ISBN
9780128117743
Erroneous ISBN
9780128117736
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Beyond pseudo-rotations in pseudo-euclidean spaces :
General Material Designation
[Book]
Other Title Information
an introduction to the theory of bi-gyrogroups and bi-gyrovector spaces /
First Statement of Responsibility
Abraham A. Ungar.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
London, United Kingdom :
Name of Publisher, Distributor, etc.
Academic Press, an imprint of Elsevier,
Date of Publication, Distribution, etc.
[2018]
Date of Publication, Distribution, etc.
©2018
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Front Cover; Beyond Pseudo-rotations in Pseudo-Euclidean Spaces: An Introduction to the Theory of Bi-gyrogroups and Bi-gyrovector Spaces Introduction to the Theory of Bi-gyrogroups and Bi-gyrovector Spaces; Copyright; Dedication; Contents; Acknowledgments; Preface; About the Author; CHAPTER 1: Introduction; 1.1. Introduction; 1.2. Quantum Entanglement and Geometric Entanglement; 1.3. From Galilei to Lorentz Transformations; 1.4. Galilei and Lorentz Transformations of Particle Systems; 1.5. Chapters of the Book; CHAPTER 2: Einstein Gyrogroups; 2.1. Introduction; 2.2. Einstein Velocity Addition.
Text of Note
2.3. Einstein Addition with Respect to Cartesian Coordinates2.4. Einstein Addition vs. Vector Addition; 2.5. Gyrations; 2.6. From Einstein Velocity Addition to Gyrogroups; 2.7. Gyrogroup Cooperation (Coaddition); 2.8. First Gyrogroup Properties; 2.9. Elements of Gyrogroup Theory; 2.10. The Two Basic Gyrogroup Equations; 2.11. The Basic Gyrogroup Cancellation Laws; 2.12. Automorphisms and Gyroautomorphisms; 2.13. Gyrosemidirect Product; 2.14. Basic Gyration Properties; 2.15. An Advanced Gyrogroup Equation; 2.16. Gyrocommutative Gyrogroups; CHAPTER 3: Einstein Gyrovector Spaces.
Text of Note
3.1. The Abstract Gyrovector Space3.2. Einstein Special Relativistic Scalar Multiplication; 3.3. Einstein Gyrovector Spaces; 3.4. Einstein Addition and Differential Geometry; 3.5. Euclidean Lines; 3.6. Gyrolines â#x80;#x93; The Hyperbolic Lines; 3.7. Gyroangles â#x80;#x93; The Hyperbolic Angles; 3.8. The Parallelogram Law; 3.9. Einstein Gyroparallelograms; 3.10. The Gyroparallelogram Law; 3.11. Euclidean Isometries; 3.12. The Group of Euclidean Motions; 3.13. Gyroisometries â#x80;#x93; The Hyperbolic Isometries; 3.14. Gyromotions â#x80;#x93; The Motions of Hyperbolic Geometry.
Text of Note
4.14. Product of Lorentz Transformations4.15. The Bi-gyrocommutative Law in Bi-gyrogroupoids; 4.16. The Bi-gyroassociative Law in Bi-gyrogroupoids; 4.17. Bi-gyration Reduction Properties in Bi-gyrogroupoids; 4.18. Bi-gyrogroups â#x80;#x93; P; 4.19. Bi-gyration Decomposition and Polar Decomposition; 4.20. The Bi-gyroassociative Law in Bi-gyrogroups; 4.21. The Bi-gyrocommutative Law in Bi-gyrogroups; 4.22. Bi-gyrogroup Gyrations; 4.23. Bi-gyrogroups are Gyrocommutative Gyrogroups; 4.24. Bi-gyrovector Spaces; 4.25. On the Pseudo-inverse of a Matrix.
Text of Note
CHAPTER 4: Bi-gyrogroups and Bi-gyrovector Spaces â#x80;#x93; P4.1. Introduction; 4.2. Pseudo-Euclidean Spaces and Pseudo-Rotations; 4.3. Matrix Representation of SO(m, n); 4.4. Parametric Realization of SO(m, n); 4.5. Bi-boosts; 4.6. Lorentz Transformation Decomposition; 4.7. Inverse Lorentz Transformation; 4.8. Bi-boost Parameter Composition; 4.9. On the Block Entries of the Bi-boost Product; 4.10. Bi-gyration Exclusion Property; 4.11. Automorphisms of the Parameter Bi-gyrogroupoid; 4.12. Squared Bi-boosts; 4.13. Commuting Relations Between Bi-gyrations and Bi-rotations.
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SUMMARY OR ABSTRACT
Text of Note
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.
TOPICAL NAME USED AS SUBJECT
Geometry, Hyperbolic.
Special relativity (Physics)
Geometry, Hyperbolic.
SCIENCE-- Energy.
SCIENCE-- Mechanics-- General.
SCIENCE-- Physics-- General.
Special relativity (Physics)
(SUBJECT CATEGORY (Provisional
SCI-- 024000
SCI-- 041000
SCI-- 055000
DEWEY DECIMAL CLASSIFICATION
Number
530
.
11
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QC173
.
65
PERSONAL NAME - PRIMARY RESPONSIBILITY
Ungar, Abraham A.
ORIGINATING SOURCE
Date of Transaction
20200822084943.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
