Overview
- Offers an axiomatic presentation of the geometric algebra of an orthogonal geometry
- Illustrates topics with a variety of examples and applications
- Relates Lipschitz spinorial groups and how they connect with the group of isometries in a non-degenerate orthogonal geometry
- Surveys major areas of application, particularly mathematics, physics and engineering
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (6 chapters)
Keywords
About this book
After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index.
Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
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Authors and Affiliations
About the author
Sebastià Xambó-Descamps is an Emeritus Full Professor of Information and Coding Theory at the Department of Mathematics of the Universitat Politècnica de Catalunya (UPC). He holds a Ph.D. in Mathematics from the University of Barcelona, and an M.Sc. degree in Mathematics from Brandeis University, USA. Has been Full Professor at the Department of Algebra of the Universidad Complutense of Madrid, President of the Catalan Mathematical Society, Dean of the Faculty of Mathematics and Statistics of the UPC and President of the Spanish Conference of Deans of Mathematics. Led various R+D+I projects, including the development of the Wiris mathematical platform. Among other productions, authored “Block Error-Correcting Codes--A Computational Primer”, co-authored "The Enumerative Theory of Conics after Halphen,” edited “Enumerative Geometry--Sitges 1987,” and co-edited “Cosmology, Quantum Vacuum and Zeta Functions”. More recently has co-authored the SpringerBrief "A GeometricAlgebra Invitation to Space-Time Physics, Robotics and Molecular Geometry".
Bibliographic Information
Book Title: Real Spinorial Groups
Book Subtitle: A Short Mathematical Introduction
Authors: Sebastià Xambó-Descamps
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-00404-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-030-00403-3Published: 29 November 2018
eBook ISBN: 978-3-030-00404-0Published: 22 November 2018
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 151
Number of Illustrations: 10 b/w illustrations, 1 illustrations in colour
Topics: Geometry, Group Theory and Generalizations, Mathematical Methods in Physics