In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional m...(展开全部)

This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of t...(展开全部)

Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and ...(展开全部)

Permutation Groups form one of the oldest parts of group theory. Through the ubiquity of group actions and the concrete representations which they afford, both finite and infinite permutation groups arise in many parts of mathematics and continue to be a lively topic of research in their own right. The book begins with the basic ideas, standard constructions and important examp...(展开全部)

Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multi...(展开全部)

Loop groups, the simplest class of infinite dimensional Lie groups, have recently been the subject of intense study. This book gives a complete and self-contained account of what is known about them from a geometrical and analytical point of view, drawing together the many branches of mathematics from which current theory developed--algebra, geometry, analysis, combinatorics, a...(展开全部)

This book is intended for a one year graduate course on Lie groups. Rather than providing a comprehensive treatment, the author emphasizes the beautiful representation theory of compact groups. However, this book also discusses important topics such as the Bruhat decomposition and the theory of symmetric spaces.

This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl ch...(展开全部)