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AuthorRosenfeld, Boris. author
TitleGeometry of Lie Groups [electronic resource] / by Boris Rosenfeld
ImprintBoston, MA : Springer US : Imprint: Springer, 1997
Connect tohttp://dx.doi.org/10.1007/978-1-4757-5325-7
Descript XVIII, 398 p. online resource

SUMMARY

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 Colยญ 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


CONTENT

0. Structures of Geometry -- I. Algebras and Lie Groups -- II. Affine and Projective Geometries -- III. Euclidean, Pseudo-Euclidean, Conformal and Pseudo conformal Geometries -- IV. Elliptic, Hyperbolic, Pseudoelliptic, and Pseudohyperbolic Geometries -- V. Quasielliptic, Quasihyperbolic, and Quasi-Euclidean Geometries -- VI. Symplectic and Quasisymplectic Geometries -- VII. Geometries of Exceptional Lie Groups. Metasymplectic Geometries -- References -- Index of Persons -- Index of Subjects


Mathematics Topological groups Lie groups Geometry Mathematics Geometry Topological Groups Lie Groups



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