Symmetry is a key factor in lots of mathematical, actual, and organic theories. utilizing illustration idea and invariant idea to investigate the symmetries that come up from staff activities, and with robust emphasis at the geometry and simple idea of Lie teams and Lie algebras, Symmetry, Representations, and Invariants is an important transforming of an prior highly-acclaimed paintings via the authors. the result's a accomplished advent to Lie idea, illustration conception, invariant thought, and algebraic teams, in a brand new presentation that's extra available to scholars and contains a broader diversity of applications.

The philosophy of the sooner booklet is retained, i.e., proposing the significant theorems of illustration idea for the classical matrix teams as motivation for the overall idea of reductive teams. The wealth of examples and dialogue prepares the reader for the total arguments now given within the basic case.

Key gains of Symmetry, Representations, and Invariants: (1) Early chapters compatible for honors undergraduate or starting graduate classes, requiring simply linear algebra, uncomplicated summary algebra, and complex calculus; (2) functions to geometry (curvature tensors), topology (Jones polynomial through symmetry), and combinatorics (symmetric workforce and younger tableaux); (3) Self-contained chapters, appendices, entire bibliography; (4) greater than 350 workouts (most with targeted tricks for options) additional discover major recommendations; (5) Serves as an exceptional major textual content for a one-year path in Lie team concept; (6) advantages physicists in addition to mathematicians as a reference work.