Geometry of Lie Groups

1. Front Matter

   Pages i-xviii

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2. Structures of Geometry

   • Boris Rosenfeld

   Pages 1-28

3. Algebras and Lie Groups

   • Boris Rosenfeld

   Pages 29-105

4. Affine and Projective Geometries

   • Boris Rosenfeld

   Pages 106-167

5. Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries

   • Boris Rosenfeld

   Pages 168-218

6. Elliptic, Hyperbolic, Pseudoelliptic, and Pseudohyperbolic Geometries

   • Boris Rosenfeld

   Pages 219-283

7. Quasielliptic, Quasihyperbolic, and Quasi-Euclidean Geometries

   • Boris Rosenfeld

   Pages 284-310

8. Symplectic and Quasisymplectic Geometries

   • Boris Rosenfeld

   Pages 311-330

9. Geometries of Exceptional Lie Groups. Metasymplectic Geometries

   • Boris Rosenfeld

   Pages 331-369

10. Back Matter

    Pages 370-397

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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

• Department of Mathematics, Pennsylvania State University, University Park, USA

  Boris Rosenfeld

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