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Real Spinorial Groups

A Short Mathematical Introduction. SpringerBriefs in Mathematics

Format: Paperback / softback
Publisher: Springer Nature Switzerland AG, Cham, Switzerland
Published: 29th Nov 2018
Dimensions: w 156mm h 234mm d 9mm
Weight: 240g
ISBN-10: 3030004031
ISBN-13: 9783030004033
Barcode No: 9783030004033
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Synopsis
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.

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"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)