Lie Groups and Algebraic Groups

Focusing on Lie groups and algebraic groups, this work was created from hectographed notes in Russian from Moscow University. It has been extended and organized to develop the material through the posing of problems and to illustrate it through a wealth of examples.

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Focusing on Lie groups and algebraic groups, this work was created from hectographed notes in Russian from Moscow University. It has been extended and organized to develop the material through the posing of problems and to illustrate it through a wealth of examples. Tables cover decomposition of representations into irreducible components, which should be useful to physicists. Topics covered include: the correspondence between Lie groups and Lie algebras; elements of algebraic geometry and of algebraic group theory over fields of real and complex numbers; and the main facts of the theory of semi-simple Lie groups (real and complex, their local and global classification included) and their representations.