Geometry of Lie Groups

  • Boris Rosenfeld

Part of the Mathematics and Its Applications book series (MAIA, volume 393)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Boris Rosenfeld
    Pages 1-28
  3. Boris Rosenfeld
    Pages 29-105
  4. Boris Rosenfeld
    Pages 106-167
  5. Boris Rosenfeld
    Pages 311-330
  6. Back Matter
    Pages 370-397

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.


Grad algebra associative algebra finite group lie group

Authors and affiliations

  • Boris Rosenfeld
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

Bibliographic information