Mathematics and Its Applications

Geometry of Lie Groups

Authors: Rosenfeld, B., Wiebe, Bill

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About this book

This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col­ lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.

Table of contents (8 chapters)

  • Structures of Geometry

    Rosenfeld, Boris

    Pages 1-28

  • Algebras and Lie Groups

    Rosenfeld, Boris

    Pages 29-105

  • Affine and Projective Geometries

    Rosenfeld, Boris

    Pages 106-167

  • Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries

    Rosenfeld, Boris

    Pages 168-218

  • Elliptic, Hyperbolic, Pseudoelliptic, and Pseudohyperbolic Geometries

    Rosenfeld, Boris

    Pages 219-283

Buy this book

eBook $139.00
price for USA in USD (gross)
  • ISBN 978-1-4757-5325-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.99
price for USA in USD
  • ISBN 978-0-7923-4390-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.99
price for USA in USD
  • ISBN 978-1-4419-4769-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Lie Groups
Authors
Series Title
Mathematics and Its Applications
Series Volume
393
Copyright
1997
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4757-5325-7
DOI
10.1007/978-1-4757-5325-7
Hardcover ISBN
978-0-7923-4390-5
Softcover ISBN
978-1-4419-4769-7
Edition Number
1
Number of Pages
XVIII, 398
Topics