Geometry of Lie Groups
Geometry of Lie Groups by B. Rosenfeld, published by Springer US on December 8, 2010, is a softcover reprint of the hardcover first edition from 1997, comprising 398 pages. This book presents the author’s extensive research in Non-Euclidean Geometries and the Geometry of Lie groups, drawing from his teaching experiences at various universities, including Moscow State University and Pennsylvania State University.
Readers will find a detailed exploration of non-Euclidean geometries, particularly as they relate to simple Lie groups. The text delves into classical non-Euclidean geometries, such as hyperbolic and elliptic forms, and discusses their interpretations in various mathematical contexts. The book aims to provide insights into the geometry of classical real non-Euclidean spaces and their representations, enhancing the understanding of complex geometrical concepts through diverse interpretations.
Official synopsis Publisher
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.
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