Specialization Of Quadratic And Symmetric Bilinear Forms

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Specialization of Quadratic and Symmetric Bilinear Forms

Author : Manfred Knebusch
Publisher : Springer Science & Business Media
ISBN 13 : 1848822421
Total Pages : 202 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Specialization of Quadratic and Symmetric Bilinear Forms by : Manfred Knebusch

Download or read book Specialization of Quadratic and Symmetric Bilinear Forms written by Manfred Knebusch and published by Springer Science & Business Media. This book was released on 2011-01-22 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematician Said Who Can Quote Me a Theorem that’s True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic forms. It is—poetic exaggeration allowed—a suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : K? L?? be a place. Then one can assign a form? (?)toaform? over K in a meaningful way ? if? has “good reduction” with respect to? (see§1.1). The basic idea is to simply apply the place? to the coe?cients of?, which must therefore be in the valuation ring of?. The specialization theory of that time was satisfactory as long as the ?eld L, and therefore also K, had characteristic 2. It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over ?elds, as can be seen from the book [26]of Izhboldin–Kahn–Karpenko–Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there).

Quadratic Forms -- Algebra, Arithmetic, and Geometry

Author : Ricardo Baeza
Publisher : American Mathematical Soc.
ISBN 13 : 0821846485
Total Pages : 424 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quadratic Forms -- Algebra, Arithmetic, and Geometry by : Ricardo Baeza

Download or read book Quadratic Forms -- Algebra, Arithmetic, and Geometry written by Ricardo Baeza and published by American Mathematical Soc.. This book was released on 2009-08-14 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.

Reviews in Number Theory 1973-83

Author : Richard K. Guy
Publisher :
ISBN 13 :
Total Pages : 844 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Reviews in Number Theory 1973-83 by : Richard K. Guy

Download or read book Reviews in Number Theory 1973-83 written by Richard K. Guy and published by . This book was released on 1984 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Quadratic Forms over Fields

Author : Tsit-Yuen Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821810952
Total Pages : 577 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Quadratic Forms over Fields by : Tsit-Yuen Lam

Download or read book Introduction to Quadratic Forms over Fields written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 2005 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.

$K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras

Author : Bill Jacob
Publisher : American Mathematical Soc.
ISBN 13 : 0821803409
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras by : Bill Jacob

Download or read book $K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1995 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of two - also available in a set of both volumes.

Index of Mathematical Papers

Author :
Publisher :
ISBN 13 :
Total Pages : 628 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Index of Mathematical Papers by :

Download or read book Index of Mathematical Papers written by and published by . This book was released on 1973 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Journal für die reine und angewandte Mathematik

Author :
Publisher :
ISBN 13 :
Total Pages : 1572 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Journal für die reine und angewandte Mathematik by :

Download or read book Journal für die reine und angewandte Mathematik written by and published by . This book was released on 1979 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Orderings, Valuations and Quadratic Forms

Author : Tsit-Yuen Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821807021
Total Pages : 158 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orderings, Valuations and Quadratic Forms by : Tsit-Yuen Lam

Download or read book Orderings, Valuations and Quadratic Forms written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 1983 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to ordered fields and reduced quadratic forms using valuation-theoretic techniques. This book describes the techniques of residue forms and the relevant Springer theory.

Quadratic and Hermitian Forms

Author : McMaster University
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860083
Total Pages : 362 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Quadratic and Hermitian Forms by : McMaster University

Download or read book Quadratic and Hermitian Forms written by McMaster University and published by American Mathematical Soc.. This book was released on 1984 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).

The Algebraic and Geometric Theory of Quadratic Forms

Author : Richard S. Elman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873229
Total Pages : 456 pages
Book Rating : 4.8/5 (732 download)

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Book Synopsis The Algebraic and Geometric Theory of Quadratic Forms by : Richard S. Elman

Download or read book The Algebraic and Geometric Theory of Quadratic Forms written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 2008-07-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

Clifford Algebras and Lie Theory

Author : Eckhard Meinrenken
Publisher : Springer Science & Business Media
ISBN 13 : 3642362168
Total Pages : 331 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Clifford Algebras and Lie Theory by : Eckhard Meinrenken

Download or read book Clifford Algebras and Lie Theory written by Eckhard Meinrenken and published by Springer Science & Business Media. This book was released on 2013-02-28 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.

Witt Rings and Ordering of Fields

Author : Thomas Curtis Craven
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Witt Rings and Ordering of Fields by : Thomas Curtis Craven

Download or read book Witt Rings and Ordering of Fields written by Thomas Curtis Craven and published by . This book was released on 1973 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ring Theory and Algebra III

Author : Bernard R. McDonald
Publisher :
ISBN 13 :
Total Pages : 454 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Ring Theory and Algebra III by : Bernard R. McDonald

Download or read book Ring Theory and Algebra III written by Bernard R. McDonald and published by . This book was released on 1980 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bulletin of the Belgian Mathematical Society, Simon Stevin

Author :
Publisher :
ISBN 13 :
Total Pages : 506 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Bulletin of the Belgian Mathematical Society, Simon Stevin by :

Download or read book Bulletin of the Belgian Mathematical Society, Simon Stevin written by and published by . This book was released on 2005 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Pacific Journal of Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 1040 pages
Book Rating : 4.:/5 (39 download)

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Book Synopsis Pacific Journal of Mathematics by :

Download or read book Pacific Journal of Mathematics written by and published by . This book was released on 1983 with total page 1040 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quadratic Mappings and Clifford Algebras

Author : Jacques Helmstetter
Publisher : Springer Science & Business Media
ISBN 13 : 3764386061
Total Pages : 512 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Quadratic Mappings and Clifford Algebras by : Jacques Helmstetter

Download or read book Quadratic Mappings and Clifford Algebras written by Jacques Helmstetter and published by Springer Science & Business Media. This book was released on 2008-05-24 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods.

Algebraic and Arithmetic Theory of Quadratic Forms

Author : Ricardo Baeza
Publisher : American Mathematical Soc.
ISBN 13 : 082183441X
Total Pages : 364 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Arithmetic Theory of Quadratic Forms by : Ricardo Baeza

Download or read book Algebraic and Arithmetic Theory of Quadratic Forms written by Ricardo Baeza and published by American Mathematical Soc.. This book was released on 2004 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.