By Brian C. Hall
This textbook treats Lie teams, Lie algebras and their representations in an straight forward yet totally rigorous style requiring minimum necessities. specifically, the idea 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 obtainable therapy of the fundamental idea of Lie teams and Lie algebras, the e-book can also be noteworthy for including:
The moment variation of Lie teams, Lie Algebras, and Representations includes many significant advancements and additions, between them: a wholly new half dedicated to the constitution and illustration conception 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 remedy of common enveloping algebras, together with an evidence of the Poincaré–Birkhoff–Witt theorem and the life of Verma modules; entire proofs of the Weyl personality formulation, the Weyl size formulation and the Kostant multiplicity formula.
Review of the 1st edition:
The Mathematical Gazette wrote:
This is a wonderful booklet. It merits to, and surely will, develop into the traditional textual content for early graduate classes in Lie workforce concept ... an immense addition to the textbook literature ... it's hugely recommended.