Groups and group theory

This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century.

According to Drinfeld, a quantum group is the same as a Hopf algebra.

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics.

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.

The field of vertex operator algebras is an active area of research and plays an integral role in infinite-dimensional Lie theory, string theory, and conformal field theory, and other subdisciplines of mathematics and physics.

Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase.

Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations.

Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions.

Conformal groups play a key role in geometry and spin structures.

Harmonic analysis is a venerable part of modern mathematics.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

The main goal of the book is to present a proof of the following.

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, algorithms and sequence design.

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics- and in theoretical physics such as quantum field theory and string theory.

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.

One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.

Hideki Omori is widely recognized as one of the world's most creative and original mathematicians.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established.

D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory.

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology.

This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?

Dedicated to Anthony Joseph, this volume contains surveys and invited articles by leading specialists in representation theory.

A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory.

Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups).

Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A.

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.

This volume contains research and survey articles by well known and respected mathematicians describing recent developments and research trends in differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields.

One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields.

The theory of Frobenius splittings has made a significant impact in the study of the geometry of flag varieties and representation theory.

The basics of group theory and its applications to themes such as the analysis of vibrational spectra and molecular orbital theory are essential knowledge for the undergraduate student of inorganic chemistry.

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact.

Geared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory.

Matrix Inequalities and Their Extensions to Lie Groups gives a systematic and updated account of recent important extensions of classical matrix results, especially matrix inequalities, in the context of Lie groups.

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress.

The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.

The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.

Symmetry is a key ingredient in many mathematical, physical, and biological theories.

"e;Mirrors and Reflections"e; presents a systematic and elementary introduction to the properties of finite groups generated by reflections.

This is a textbook on Galois theory.

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds.

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact.

This text started out as a revised version of Buildings by the second-named author [53], but it has grown into a much more voluminous book.

This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices.

This book is a monograph on unitals embedded in ?

In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates.

Aimed at advanced undergraduates and graduate students, this book is about the interplay between algebraic topology and the theory of infinite discrete groups.

After a few initial chapters on the basics of Mathematica, the logic of the book is controlled by group theory.

About the first edition: The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules.