Kategoria BISAC: Mathematics >> Group Theory

A systematic survey of all the basic results on the theory of discrete subgroups of Lie groups, presented in a convenient form for users. The book makes the theory accessible to a wide audience, and will be a standard reference for many years to come.

This book contains the proceedings of a meeting that brought together friends and colleagues of Guy Rideau at the Universite Denis Diderot (Paris, France) in January 1995.
It contains original results as well as review papers covering important domains of mathematical physics, such as modern statistical mechanics, field theory, and quantum groups. The emphasis is on geometrical approaches. Several papers are devoted to the study of symmetry groups, including applications to nonlinear differential equations, and deformation of structures, in particular deformation-quantization and...

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The past several years have witnessed a striking number of important developments in Complex Analysis. One of the characteristics of these developments has been to bridge the gap existing between the theory of functions of one and of several complex variables. The Special Year in Complex Analysis at the University of Maryland, and these proceedings, were conceived as a forum where these new developments could be presented and where specialists in different areas of complex analysis could exchange ideas. These proceedings contain both surveys of different subjects covered during the year as...

Sets out to study the notion of a local moduli suite of algebraic objects like schemes, singularities or Lie algebras. This book addresses mathematicians working on problems of moduli, in algebraic or in complex analytic geometry.

This is a textbook on Galois theory. Galois theory has a well-deserved re- tation as one of the most beautiful subjects in mathematics. I was seduced by its beauty into writing this book. I hope you will be seduced by its beauty in reading it. This book begins at the beginning. Indeed (and perhaps a little unusually for a mathematics text), it begins with an informal introductory chapter, Ch- ter 1. In this chapter we give a number of examples in Galois theory, even before our terms have been properly de?ned. (Needless to say, even though we proceed informally here, everything we say is...

This book is a monograph on unitals embedded in ?nite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are many open pr- lems, and this remains a fruitful area for Ph.D. dissertations. Unitals play an important role in ?nite geometry as well as in related areas of mathematics. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order...

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." A historical note provides a survey of the contexts in which groups generated by reflections have arisen. A brief introduction includes almost the only other mention of Lie groups and algebras to be found in the volume. Thus the presentation here is really quite...

The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups.

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce premier volume du Livre de Topologie generale, troisieme Livre du traite, est consacre aux structures fondamentales en topologie, qui constituent les fondement de l analyse et de la geometrie. Il comprend les chapitres: 1. Structures topologiques; 2. Structures uniformes; 3. Groupes topologiques; 4. Nombres reels.

Il contient egalement des notes historiques.

Ce...

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce premier volume du Livre d Algebre commutative, septieme Livre du traite, est consacre aux concepts fondamentaux de l algebre commutative. Il comprend les chapitres: 1. Modules plats; 2. Localisation; 3. Graduations, filtrations et topologies; 4. Ideaux premiers associes et decomposition primaire.

Il contient egalement des notes historiques.

Ce volume est une reimpression de l edition de 1969.

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Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce troisieme volume du Livre sur les Groupes et algebres de Lie, neuvieme Livre du traite, poursuit l etude des algebres de Lie et leurs representations.

Il comprend les chapitres: 7. Sous-algebres de Cartan, elements reguliers; 8. Algebres de Lie semi-simples deployees.

Ce volume contient egalement un appendice sur la topologie de Zariski.

Ce volume est une reimpression de...

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce deuxieme volume du Livre d Algebre commutative, septieme Livre du traite, introduit deux notions fondamentales en algebre commutative, celle d entier algebrique et celle de valuation, qui ont de nombreuses applications en theorie des nombres et en geometrie algebrique. It traite egalement des anneaux de Krull ou de Dedekind. Il comprend les chapitres: 1. Entiers; 2. Valuations; 3. Diviseurs.

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Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce volume du Livre d Algebre commutative, septieme Livre du traite, comprend les chapitres: 1. Dimension; 2. Anneaux locaux noetheriens complets.

Le chapitre 8 traite de diverses notions de dimension en algebre commutative, telles que la dimension de Krull d un anneau. Ces notions jouent un role capital en geometrie algebrique. Le chapitre 9 introduit, quant a lui, les vecteurs de Witt et...

From the reviews:
..". They (Gabriel and Roiter) are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature. ..." The Mathematical Gazette, 1993
..". The standard of this text is high and will be definitely appreciated by the algebraic community." Monatshefte Mathematik, 1994
.."This book is...

A basic problem in geometry is to ?nd canonical metrics on smooth manifolds. Such metrics can be speci?ed, for instance, by curvature conditions or extremality properties, and are expected to contain basic information on the topology of the underlying manifold. Constant curvature metrics on surfaces are such canonical metrics. Their distinguished role is emphasized by classical uniformization theory. Amorerecentcharacterizationofthesemetrics describes them ascriticalpoints of the determinant functional for the Laplacian.The key tool here is Polyakov'sva- ationalformula for the determinant. In...

The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I. I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, .. This part has been written with the help of F.Raggi and J.Tate. I want to thank them, and also Sue Golan, who did the typing for both parts....

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce premier volume du Livre sur les Groupes et algebre de Lie, neuvieme Livre du traite, est consacre aux concepts fondamentaux pour les algebres de Lie. Il comprend les paragraphes: - 1 Definition des algebres de Lie; 2 Algebre enveloppante d une algebre de Lie; 3 Representations; 4 Algebres de Lie nilpotentes; 5 Algebres de Lie resolubles; 6 Algebres de Lie semi-simples; 7 Le theoreme d Ado.

Ce...