Lie Groups

Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis.

Key to this unique exposition is the large amount of background material presented so the book is accessible to a reader with relatively modest mathematical background. Historical information, examples, exercises are all woven into the text.

Lie Groups: An Approach through Invariants and Representations will engage a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.

Covers a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, lie groups and lie algebras, tensor algebra and symmetry, semisimple lie algebras, algebraic groups, group representations, invariants, Hilbert theory, binary forms with fields ranging from pure algebra to functional analysis Extensive treatment of classical groups, not covered in other texts Author's mastery of the subject reflected in the depth and quality of this work Sufficient background material is covered; book is accessible to a reader with relatively modest mathematical background

Contenu
General Methods and Ideas.- Symmetric Functions.- Theory of Algebraic Forms.- Lie Algebras and lie Groups.- Tensor Algebra.- Semisimple Algebras.- Algebraic Groups.- Group Representations.- Tensor Symmetry.- Semisimple Lie Groups and Algebras.- Invariants.- Tableaux.- Standard Monomials.- Hilbert Theory.- Binary Forms.