Lie Algebras and Algebraic Groups
The main topic of this comprehensive monograph is a detailed study of Lie algebras over an algebraically closed field of zero characteristic. The first ten chapters summarize basic results from commutative algebra, topology, sheaf theory, Jordan decomposition and basic facts on groups and their representations. The following seven chapters review required facts from algebraic geometry. The next part of the book (nine chapters) contains a detailed study of the relationship between algebraic groups and corresponding Lie algebras. The next two chapters contain the theory of representations of semisimple Lie algebras and the Chevalley theorem on invariants. Then the author introduces S-triples and describes properties of nilpotent orbits in semisimple Lie algebras. The final chapters are devoted to symmetric Lie algebras, semisimple symmetric Lie algebras, sheets of Lie algebras and a study of properties of the coadjoint representation. The main advantage of the book is a systematic treatment of the field, including detailed proofs.