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...
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 ad...
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.
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 ver...
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.
Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal ...
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
Describes the structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. This book presen...
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
Develops an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operat...
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...
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 ...
The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These series were first studied systematically by Heine, but many early results are attributed to Euler, Gauss, and Jacobi. This book provides a simple approach to basic hypergeometric series.
The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These ...
Louis de Branges of Purdue University is recognized as the mathematician who proved Bieberbach's conjecture. This book offers insight into the nature of the conjecture, its history and its proof. It is suitable for research mathematicians and analysts.
Louis de Branges of Purdue University is recognized as the mathematician who proved Bieberbach's conjecture. This book offers insight into the nature ...
Around 1980, G Mason announced the classification of a certain subclass of a class of finite simple groups known as 'quasithin groups'. The classification of the finite simple groups depends upon a proof that there are no unexpected groups in this subclass
Around 1980, G Mason announced the classification of a certain subclass of a class of finite simple groups known as 'quasithin groups'. The classifica...
The Teichmuller space T(X) is the space of marked conformal structures on a given quasiconformal surface X. This volume uses quasiconformal mapping to give a unified and up-to-date treatment of T(X). Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type. The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to three-dimensional manifolds through its relationship to Kleinian...
The Teichmuller space T(X) is the space of marked conformal structures on a given quasiconformal surface X. This volume uses quasiconformal mapping to...