The subject of amenability has its roots in the work of Lebesgue at the turn of the century. In the 1940s, the subject began to shift from finitely additive measures to means. This shift is of fundamental importance, for it makes the substantial resources of functional analysis and abstract harmonic analysis available to the study of amenability. The ubiquity of amenability ideas and the depth of the mathematics involved points to the fundamental importance of the subject. This book presents a comprehensive and coherent account of amenability as it has been developed in the large and varied...

A careful exposition of a research field of current interest. This includes a brief survey of the subject and an introduction to recent developments and unsolved problems.

The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.

Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.

Describes the structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. This book presents an analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Mori

This text explores the surprisingly complex structure of free lattices. The first part of the book presents a complete exposition of the basic theory of free lattices, projective lattices, and lattices which are bounded homomorphic images of a free lattice, as well as applications of these results to other areas. This portion of the book is suitable for use in a graduate course in lattice theory or general algebra. The second part of the book contains new results about free lattices and new proofs of known results, providing the reader with a coherent picture of the fine structure of free...

Develops an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a 'Fermat quotient operator', and differential equations (viewed as functions on jet spa

This text is an exposition of what is known about the fundamental groups of compact Kahler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. This book collects together results obtained in recent years which aim to characterize those infinite groups which can arise as fundamental groups of compact Kahler manifolds. Most of these results are negative ones, saying which groups do not arise. The methods and techniques used form a mix of topology, differential and algebraic geometry, and complex analysis. The book...

Presents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities. This book features Gromov's inequalities and their generalisations, as well as asymptotic phenomena for systoles of surfaces of large genus, revealing

Suitable for researchers in ring theory or allied topics, such as the representation theory of finite dimensional Lie algebras, this book presents advances in ring theory and their applications to other areas. It includes such topics as the structure of group rings of polycyclic-by-finite groups, and localization in non commutative rings.