Real Spinorial Groups : A Short Mathematical Introduction. 1st ed. 2018

種類:

電子ブック

責任表示:

by Sebastià Xambó-Descamps

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Xambó-Descamps, Sebastià.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9783030004040 [303000404X]    

注記:

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.
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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