Kategoria BISAC: Mathematics >> Algebra - Linear

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, deuxieme Livre des Elements de mathematique, traite notamment des extensions de corps et de la theorie de Galois. Il comprend les chapitres: 4. Polynomes et fractions rationnelles; 5. Corps commutatifs; 6. Groupes et corps ordonnes; 7. Modules sur les anneaux principaux.

Il contient egalement des notes historiques.

Ce volume est une nouvelle edition parue en...

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

Ce dixieme chapitre du Livre d Algebre, deuxieme Livre du traite, pose les bases du calcul homologique.

Ce volume est a ete publie en 1980.

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Formes sesquilineaires et formes quadratiques

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

Ce neuvieme chapitre du Livre d'Algebre, deuxieme Livre du traite, est consacre aux formes quadratiques, symplectiques ou hermitiennes et aux groupes associes.

Il contient egalement une note historique.

Ce volume est une reimpression de l'edition de 1959.

On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations .2 .2 1 Z =] = -, ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized...

In the book there are introduced models and methods of construction of pseudo-solutions for the well-posed and ill-posed linear functional equations circumscribing models passive, active and complicated experiments. Two types of the functional equations are considered: systems of the linear algebraic equations and linear integral equations. Methods of construction of pseudos6lutions are developed in the presence of passive right-hand side errors for two types of operator errors: passive measurements and active representation errors of the operator, and all their combinations. For the...

As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras.

Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent...

This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

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....

This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields.

This title gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory....

This first part of this two-volume work presents an introduction to functional analysis and the initial fundamentals of C ]* - and Von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Well supplied with exercises, the text assumes only basic measure theory and topology. The books present the possibility for the design of numerous courses aimed at different audiences.

An expanded edition of Kac's original introduction to algebraic aspects of conformal field theory which was published by the AMS in 1996. This revised edition is based on courses given by the author at MIT and at Rome University in Spring 1997. New material is added, including the foundations of a rapidly growing area of algebraic conformal theory. Also, in some places, the exposition is significantly simplified.

Free probability theory is a highly noncommutative probability theory, with independence based on free products instead of tensor products. The theory models random matrices in the large N limit and operator algebra free products. It has led to a surge of new results on the von Neumann algebras of free groups. This is a volume of papers from a workshop on Random Matrices and Operator Algebra Free Products, held at the Fields Institute for Research in the Mathematical Sciences in March 1995. Over the last few years, there has been much progress on the operator algebra and noncommutative...

Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over $p$-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very...

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics: algebra, differential geometry, algebraic geometry, analysis, and differential equations. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry...

The Ausdehnungslehre of 1862 is Grassmann's most mature presentation of his extension theory and captured the full sweep of his mathematical achievements. Compared with Grassmann's first book, Lineale Ausdehnungslehre, this book contains new material, including a detailed development of the inner product and its relation to the concept of angle, the theory of functions from the point of view of extension theory, and Grassmann's contribution to the Pfaff problem. In many ways, this book is the version of Grassmann's system most accessible to contemporary readers.

Presents an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. This book contains several topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.

There are a number of very good books available on linear algebra. From this one might deduce that the existing books contain all that one needs to know in the best possible form and that any new book would just repeat material in the old ones. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many linear algebra results obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In...

Eugene Dynkin is a rare example of a contemporary mathematician who has achieved results in two quite different areas of research: algebra and probability. In both areas, his ideas constitute an essential part of modern mathematical knowledge and form a basis for further development. Although his last work in algebra was published in 1955, his contributions continue to influence current research in algebra and in the physics of elementary particles. His work in probability is part of both the historical and the modern development of the topic.

Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. Written for students with some mathematical maturity and an interest in abstraction and formal reason