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Real Spinorial Groups: A Short Mathematical Introduction
Paperback
Series: Springerbriefs in Mathematics
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ISBN10: 3030004031
ISBN13: 9783030004033
Publisher: Springer Nature
Published: Nov 29 2018
Pages: 151
Weight: 0.53
Height: 0.35 Width: 6.14 Depth: 9.21
Language: English
ISBN13: 9783030004033
Publisher: Springer Nature
Published: Nov 29 2018
Pages: 151
Weight: 0.53
Height: 0.35 Width: 6.14 Depth: 9.21
Language: English
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.
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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