By Brian C. Hall

This textbook treats Lie teams, Lie algebras and their representations in an simple yet totally rigorous style requiring minimum must haves. specifically, the speculation of matrix Lie teams and their Lie algebras is built utilizing basically linear algebra, and extra motivation and instinct for proofs is supplied than in such a lot vintage texts at the subject.

In addition to its available remedy of the elemental idea of Lie teams and Lie algebras, the publication can also be noteworthy for including:

The moment version of Lie teams, Lie Algebras, and Representations includes many sizeable advancements and additions, between them: a wholly new half dedicated to the constitution and illustration idea of compact Lie teams; a whole derivation of the most homes of root platforms; the development of finite-dimensional representations of semisimple Lie algebras has been elaborated; a therapy of common enveloping algebras, together with an explanation of the Poincaré–Birkhoff–Witt theorem and the life of Verma modules; entire proofs of the Weyl personality formulation, the Weyl measurement formulation and the Kostant multiplicity formula.

**Review of the 1st edition:**

**The Mathematical Gazette** wrote:

This is a wonderful booklet. It merits to, and absolutely will, develop into the traditional textual content for early graduate classes in Lie staff thought ... a major addition to the textbook literature ... it truly is hugely recommended.