Brian Hall – författare

'Here is art which conceals art, and intellect which conceals intellect, so that by the end of the book one feels that one understands something one had not understood before. Mr Hall is witty and amusing, but not snide; he has a lightness of touch which allows him to write of extremely serious matters without solemnity; he knows how to convey a great deal in a few words' Sunday Telegraph'He is an observant and witty writer...you believe implicitly that he has met the people he writes about, and that they said what he quotes them as saying' Sunday Times

Burnley is probably best known as an industrial town, but it is surrounded by beautiful Pennine moorland and it is here that the remains left by the first, prehistoric inhabitants of the area are to be found. The town itself had its origins in a Saxon settlement and in 1994 it celebrated the 700th anniversary of the granting of its market charter. However, the old town was transformed during the 19th century into a major centre of industry. By the turn of the century, Burnley could claim to be the cotton-weaving capital of the world, with 100,000 looms in the area producing a greater length of cloth each year than in any other place.

The golden age of Himalayan mountaineering, from the mid-1970s to the 1980s, brought forth a generation of radical young climbers. With tiny budgets and high ambitions they pioneered fast and light, alpine-style expeditions on mountains such as Jannu, Nuptse, Everest and K2.In High Risk, Brian Hall recalls the outrageous adventures of eleven of his climbing friends who risked – and often lost – their lives to stand on some of the world’s highest peaks during a legendary period in mountaineering history.

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebrasmotivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C)an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebrasa self-contained construction of the representations of compact groups, independent of Lie-algebraic argumentsThe second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.Review of the first edition:This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition tothe textbook literature ... it is highly recommended.— The Mathematical Gazette