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This series has established itself as a valuable source of information for professional mathematicians and research workers in all areas of mathematics. Most of the volumes are short monographs giving an authoritative account of the present state of knowledge of a topic of current interest. The treatment may be informal but importance is attached to clear yet rigorous exposition. The series also accepts conference proceedings and similar collective works that meet its general objectives.

  • Managing Editors: Endre Süli, University of Oxford
  • Associate Editors: Tim Austin, University of Warwick, Roger Heath-Brown, University of Oxford, Colva Roney-Dougal, University of St Andrews, Ulrike Tillmann, University of Oxford, Kasia A. Rejzner, University of York

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465 results in London Mathematical Society Lecture Note Series

Page 8 of 24

Finite Group Algebras and their Modules
  • P. Landrock
  • Published online:
    05 April 2013
    Print publication:
    29 December 1983
  • Originally published in 1983, the principal object of this book is to discuss in detail the structure of finite group rings over fields of characteristic, p, P-adic rings and, in some cases, just principal ideal domains, as well as modules of such group rings. The approach does not emphasize any particular point of view, but aims to present a smooth proof in each case to provide the reader with maximum insight. However, the trace map and all its properties have been used extensively. This generalizes a number of classical results at no extra cost and also has the advantage that no assumption on the field is required. Finally, it should be mentioned that much attention is paid to the methods of homological algebra and cohomology of groups as well as connections between characteristic 0 and characteristic p.

Commutative Algebra
  • J. T. Knight
  • Published online:
    05 April 2013
    Print publication:
    31 October 1971
  • This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.

Algebraic, Extremal and Metric Combinatorics 1986
  • Edited by M. M. Deza, P. Frankl, I. G. Rosenberg
  • Published online:
    05 April 2013
    Print publication:
    25 August 1988
  • This book represents a comprehensive overview of the present state of progress in three related areas of combinatorics. It comprises selected papers from a conference held at the University of Montreal. Topics covered in the articles include association schemes, extremal problems, combinatorial geometrics and matroids, and designs. All the papers contain new results and many are extensive surveys of particular areas of research. Particularly valuable will be Ivanov's paper on recent Soviet research in these areas. Consequently this volume will be of great attraction to all researchers in combinatorics and to research students requiring a rapid introduction to some of the open problems in the subject.

Groups and Geometry
  • Roger C. Lyndon
  • Published online:
    05 April 2013
    Print publication:
    14 March 1985
  • This book, which was originally published in 1985 and has been translated and revised by the author from notes of a course, is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and, whilst keeping the presentation at a level that assumes only a basic background in mathematics, leads the reader to the frontiers of current research at the time of publication. The treatment is concrete and combinatorial with a minimal use of analytic geometry. In the interest of the reader's intuition, most of the geometry considered is two-dimensional and there is an emphasis on examples, both in the text and in the problems at the end of each chapter.

Stable Groups
  • F. Wagner
  • Published online:
    05 April 2013
    Print publication:
    21 August 1997
  • The study of stable groups connects model theory, algebraic geometry and group theory. It analyses groups which possess a certain very general dependence relation (Shelah's notion of 'forking'), and tries to derive structural properties from this. These may be group-theoretic (nilpotency or solubility of a given group), algebro-geometric (identification of a group as an algebraic group), or model-theoretic (description of the definable sets). In this book, the general theory of stable groups is developed from the beginning (including a chapter on preliminaries in group theory and model theory), concentrating on the model- and group-theoretic aspects. It brings together the various extensions of the original finite rank theory under a unified perspective and provides a coherent exposition of the knowledge in the field.

General Cohomology Theory and K-Theory
  • P. J. Hilton
  • Published online:
    05 April 2013
    Print publication:
    28 February 1971
  • These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences.

Numerical Ranges II
  • F. F. Bonsall, J. Duncan
  • Published online:
    05 April 2013
    Print publication:
    02 August 1973
  • Numerical Ranges II is a sequel to Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by the same authors and published in this series in 1971. The present volume reflects the progress made in the subject, expanding and discussing topics under the general headings of spatial and algebra numerical ranges and further ranges.

Homogeneous Structures on Riemannian Manifolds
  • F. Tricerri, L. Vanhecke
  • Published online:
    05 April 2013
    Print publication:
    23 June 1983
  • The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail.Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

FPF Ring Theory
  • Faithful Modules and Generators of Mod-R
  • Carl Faith, Stanley Page
  • Published online:
    05 April 2013
    Print publication:
    26 April 1984
  • This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the work of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, K. Morita, T. Nakayama, R. Thrall, and more recently, W. Brandal, R. Pierce, T. Shores, R. and S. Wiegand and P. Vamos, among others. FPF rings include quasi-Frobenius rings (and thus finite rings over fields), pseudo-Frobenius (PF) rings (and thus injective cogenerator rings), bounded Dedekind prime rings and the following commutative rings; self-injective rings, Prufer rings, all rings over which every finitely generated module decomposes into a direct sum of cyclic modules (=FGC rings), and hence almost maximal valuation rings. Any product (finite or infinite) of commutative or self-basic PFP rings is FPF. A number of important classes of FPF rings are completely characterised including semiprime Neotherian, semiperfect Neotherian, perfect nonsingular prime, regular and self-injective rings. Finite group rings over PF or commutative injective rings are FPF. This work is the culmination of a decade of research and writing by the authors and includes all known theorems on the subject of noncommutative FPF rings. This book will be of interest to professional mathematicians, especially those with an interest in noncommutative ring theory and module theory.

New Developments in Topology
  • Edited by Graeme Segal
  • Published online:
    05 April 2013
    Print publication:
    28 February 1974
  • Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in June 1972 have revised their contributions and submitted them for publication in this volume. The present papers do not necessarily closely correspond with the original talks, as it was the intention of the volume editor to make this book of mathematical rather than historical interest. The contributions will be of value to workers in topology in universities and polytechnics.

Homotopy Theory: Proceedings of the Durham Symposium 1985
  • Edited by E. Rees, J. D. S. Jones
  • Published online:
    05 April 2013
    Print publication:
    29 October 1987
  • This 1987 volume presents a collection of papers given at the 1985 Durham Symposium on homotopy theory. They survey recent developments in the subject including localisation and periodicity, computational complexity, and the algebraic K-theory of spaces.

Algebraic Cycles and Motives
  • Volume 2
  • Edited by Jan Nagel, Chris Peters
  • Published online:
    05 April 2013
    Print publication:
    03 May 2007
  • Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity. This book is one of two volumes that provide a self-contained account of the subject as it stands. Together, the two books contain twenty-two contributions from leading figures in the field which survey the key research strands and present interesting new results. Topics discussed include: the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers and students in complex algebraic geometry and arithmetic geometry will find much of interest here.

A Local Spectral Theory for Closed Operators
  • Ivan N. Erdelyi, Wang Shengwang
  • Published online:
    05 April 2013
    Print publication:
    01 August 1985
  • This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.

Groups St Andrews 1989
  • Volume 1
  • Edited by C. M. Campbell, E. F. Robertson
  • Published online:
    05 April 2013
    Print publication:
    21 March 1991
  • These volumes contain selected papers presented at the international conference on group theory held in St Andrews in 1989. The themes of the conference were combinatorial and computational group theory; four leading group theorists (J. A. Green, N. D. Gupta, O. H. Kegel and J. G. Thompson) gave courses whose content is reproduced here. Also included are refereed papers presented at the meeting. The many articles with their wealth of references demonstrate the richness and vitality of modern group theory and its varied connections with other areas of mathematics. These will be essential references for research and postgraduate mathematicians whose work involves group theory.

Singularity Theory
  • V. I. Arnold
  • Published online:
    05 April 2013
    Print publication:
    17 September 1981
  • Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis. In this volume are collected seven of his survey articles from Russian Mathematical Surveys on singularity theory, the area to which he has made most contribution. These surveys contain Arnold's own analysis and synthesis of a decade's work. All those interested in singularity theory will find this an invaluable compilation. Professor C. T. C. Wall has written an introduction outlining the significance and content of the articles.

Conformal Fractals
  • Ergodic Theory Methods
  • Feliks Przytycki, Mariusz Urbański
  • Published online:
    05 April 2013
    Print publication:
    06 May 2010
  • This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.

Affine Sets and Affine Groups
  • D. G. Northcott
  • Published online:
    05 April 2013
    Print publication:
    08 May 1980
  • In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

Lectures on Bochner-Riesz Means
  • Katherine Michelle Davis, Yang-Chun Chang
  • Published online:
    05 April 2013
    Print publication:
    12 November 1987
  • This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 1970s, beginning with Fefferman's famous disc counterexample. The culminating chapter presents Cordoba's geometric theory of Kayeka maximal functions and multipliers. Research workers in the fields of Fourier analysis and harmonic analysis will find this a valuable account of these developments. Second year graduate students, who are familiar with Lebesgue theory and are acquainted with distributions, will be able to use this as a textbook which will bring them up to the exciting open questions in the field.

Introduction to Uniform Spaces
  • I. M. James
  • Published online:
    05 April 2013
    Print publication:
    03 May 1990
  • This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.

Representation Theory of Lie Groups
  • M. F. Atiyah, R. Bott, S. Helgason, D. Kazhdan, B. Kostant, G. Lustztig
  • Published online:
    05 April 2013
    Print publication:
    31 January 1980
  • Lie groups and their representations occupy an important place in mathematics with applications in such diverse fields as differential geometry, number theory, differential equations and physics. In 1977 a symposium was held in Oxford to introduce this rapidly developing and expanding subject to non-specialists. This volume contains the lectures of ten distinguished mathematicians designed to provide the reader with a deeper understanding of the fundamental theory and appreciate the range of results. This volume contains much to interest mathematicians and theoretical physicists from advanced undergraduate level upwards.

Page 8 of 24