About this book
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.
orthogonal geometry geometric algebra orthogonal groups spinorial groups geometric covariance
- DOI https://doi.org/10.1007/978-3-030-00404-0
- Copyright Information The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-030-00403-3
- Online ISBN 978-3-030-00404-0
- Series Print ISSN 2191-8198
- Series Online ISSN 2191-8201
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