Vinberg, Eh. B.; Gorbatsevich, V. V.; Onishchik, A. L. Structure of Lie groups and algebras. (Russian) Zbl 0733.22003 Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 41, 259 p. (1990). This attractive little book on the structure of Lie groups and Lie algebras should be translated. It is very thorough, yet concise and readable and everything very explicit. It covers just the structure and classification problems in more detail than most books, but without going into representations. The Chapters are: 1) General theorems, 2) Solvable Lie groups and algebras. 3) Complex semisimple Lie groups and algebras. 4) Real semisimple Lie groups and algebras. 5) Exceptional Lie algebras. 6) Subgroups and subalgebras of Lie groups and Lie algebras. 7) On classification of arbitrary Lie groups and algebras of a given dimension. Each chapter has well organized sections and subsections. Reviewer: A.O.Barut (Boulder) Cited in 3 ReviewsCited in 49 Documents MSC: 22E10 General properties and structure of complex Lie groups 22-02 Research exposition (monographs, survey articles) pertaining to topological groups 17B05 Structure theory for Lie algebras and superalgebras 17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras 22E15 General properties and structure of real Lie groups 22E25 Nilpotent and solvable Lie groups 17B25 Exceptional (super)algebras Keywords:Lie groups; Lie algebras; structure and classification; Solvable Lie groups; Complex semisimple Lie groups; Real semisimple Lie groups; Exceptional Lie algebras PDFBibTeX XML