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This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry.
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.
List of contents
Chapter 1- Mathematical background.- Chapter 2- Grassmann algebra.- Chapter 3- Geometric Algebra.- Chapter 4- Orthogonal geometry with GA.- Chapter 5- Zooming in on rotor groups.- Chapter 6- Postfaces.- References.
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".
Summary
This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry.
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.
Report
"This ... textbook gives an excellent introduction to real spinor groups very suitable for senior students, graduate and postgraduate students, mathematicians, physicists, computer graphics developers and mathematically interested engineers who seek information on this important and still rapidly developing subject." (Eckhard M. S. Hitzer, Mathematical Reviews, February, 2020)
