This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.
This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which t...
FC-Groups (Chapman & Hall/CRC Research Notes in Mathematics)
by M.J. Tomkinson
Lie Groups and Lie Algebras (Elements of Mathematics)
by Nicolas Bourbaki
From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or 'Tits systems'". --G.B. Seligman in MathReviews.
Semigroups. Theory and Applications (Lecture Notes in Mathematics, #1320)
Essays in Group Theory (Mathematical Sciences Research Institute Publications, #8)
Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallin...
A Singular Introduction to Commutative Algebra
by Eberhard Zeidler, Gert-Martin Greuel, and Gerhard Pfister
This book can be understood as a model for teaching commutative algebra, taking into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, it is shown how to handle it by computer. The computations are exemplified with the computer algebra system Singular developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The bo...
The aim of this monograph is to give an overview of various classes of in?ni- dimensional Lie groups and their applications, mostly in Hamiltonian - chanics, ?uid dynamics, integrable systems, and complex geometry. We have chosen to present the unifying ideas of the theory by concentrating on speci?c typesandexamplesofin?nite-dimensionalLiegroups. Ofcourse,theselection of the topics is largely in?uenced by the taste of the authors, but we hope thatthisselectioniswideenoughtodescribevariousphenom...
Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics, #94)
by Frank W Warner
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.
Lie Groups beyond an Introduction (Progress in Mathematics, #140)
by A.W. Knapp
Merging algebra and analysis, this text uses Lie-theoretic methods to develop a theory with wide applications in mathematics and physics. It aims to encourage the reader's understanding of Lie theory to evolve from beginner to expert. Topics include: the Cartan theory of complex semisimple Lie algebras; the Cartan-Weyl theory of the structure of representations of compact Lie groups; the classification of real semisimple Lie algebras; the structure theory of noncompact reductive Lie groups; and...
The Cohomology of Groups (Oxford Mathematical Monographs)
by Leonard Evens
This book presents an account of the theory of the cohomology ring of a finite group. The aim is to present a modern approach from the point of view of homological algebra, and the volume covers themes such as finite generation theorems, the cohomology of wreath products, the norm map, and variety theory. Prerequisites comprise a familiarity with modern algebra and homological algebra as might be gained from introductory graduate courses, though otherwise the book is self-contained. As a result...
Topics in Factorization of Abelian Groups (Texts and Readings in Mathematics)
by Sandor Szabo
Classification DES Groupes Algebriques Semi-Simples (Collected works of Claude Chevalley, v.3)
by Claude C. Chevalley
Le texte de cet ouvrage correspond au Seminaire dirige par Claude Chevalley, a l'Ecole Normale Superieure de Paris, pendant les annees universitaires 1956/57 et 1957/58."
Finitely Generated Commutative Monoids
by J.C. Rosales and P. A. Garcia-Sanchez
There is a lack of effective methods for studying properties of finitely generated commutative monoids. This was one of the main reasons for developing a self-contained book on finitely generated commutative monoids with the theory and algorithms needed for the study of the main classical problems related to this kind of monoid. This book is not only addressed to people working in Semigroup Theory. The only knowledge required to follow and understand its contents is basic Linear Algebra. This mo...
Poisson Structures (Grundlehren der mathematischen Wissenschaften, #347)
by Camille Laurent-Gengoux, Anne Pichereau, and Pol Vanhaecke
Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson...
Schaum's Outline of Probability, Second Edition
by Seymour Lipschutz and Marc Lipson
The ideal review for your probability courseMore than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice. Outline format supplies a concise gui...
p-Adic Methods and Their Applications
A number of texts have recently become available which provide good general introductions to p-Adic numbers and p-Adic analysis. However, there is at present a gap between such books and the sophisticated applications in the research literature. The aim of this book is to bridge this gulf by providing a collection of intermediate level articles on various applications of p-Adic techniques throughout mathematics. The idea for producing such a volume was suggested by Oxford University Press in...
In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings...
Galois Groups and Their Representations (Advanced Studies in Pure Mathematics)
This volume centres around the structure and the representations of the Galois groups of local or global fields including higher dimensional fields.