Quadratic Algebras
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Quadratic Algebras
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Author : Alexander Polishchuk
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Quadratic Algebras written by Alexander Polishchuk and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This book introduces recent developments in the study of algebras defined by quadratic relations. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, non commutative geometry, $K$-theory, number theory, and non commutative linear algebra.The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincare-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes. The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.
Quadratic Algebras Clifford Algebras And Arithmetic Witt Groups
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Author : Alexander J. Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quadratic Algebras Clifford Algebras And Arithmetic Witt Groups written by Alexander J. Hahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.
Quadratic Mappings And Clifford Algebras
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Author : Jacques Helmstetter
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-24
Quadratic Mappings And Clifford Algebras written by Jacques Helmstetter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-24 with Mathematics categories.
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.
Quadratic Algebras Clifford Algebras And Arithmetic Witt Groups
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Author : Alexander J Hahn
language : en
Publisher:
Release Date : 1993-12-17
Quadratic Algebras Clifford Algebras And Arithmetic Witt Groups written by Alexander J Hahn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-17 with categories.
Tame Algebras And Integral Quadratic Forms
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Author : Claus M. Ringel
language : en
Publisher: Springer
Release Date : 2006-11-14
Tame Algebras And Integral Quadratic Forms written by Claus M. Ringel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The Arithmetics Of Quadratic Jordan Algebras
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Author : Michel L. Racine
language : en
Publisher: American Mathematical Soc.
Release Date : 1973
The Arithmetics Of Quadratic Jordan Algebras written by Michel L. Racine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algèbres associatives categories.
The first step in obtaining an arithmetic theory for finite dimensional quadratic Jordan algebras over the quotient field of a Dedekind ring is the determination of maximal orders. This is the main concern of this paper. Jordan analogues of some of the first theorems in classical associative arithmetic are obtained. For special quadratic Jordan algebras, the problem of determining maximal orders is reduced to arithmetic questions in quadratic forms and associative algebras with involution. The number of isomorphism classes of maximal orders is computed for most central simple quadratic Jordan algebras over a local field. In the process, previous results of Knebusch are obtained in a uniform fashion and are extended to the case of algebras over fields of characteristic 2 and 3.
K Theory And Algebraic Geometry Connections With Quadratic Forms And Division Algebras
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Author : Bill Jacob
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
K Theory And Algebraic Geometry Connections With Quadratic Forms And Division Algebras written by Bill Jacob and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Volume 2 of two - also available in a set of both volumes.
Quadratic Forms Linear Algebraic Groups And Cohomology
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Author : Skip Garibaldi
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-16
Quadratic Forms Linear Algebraic Groups And Cohomology written by Skip Garibaldi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-16 with Mathematics categories.
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.
Quadrangular Algebras Mn 46
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Author : Richard M. Weiss
language : en
Publisher: Princeton University Press
Release Date : 2009-02-09
Quadrangular Algebras Mn 46 written by Richard M. Weiss and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Mathematics categories.
This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms.
Introduction To Quadratic Forms Over Fields
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Author : Tsit-Yuen Lam
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Introduction To Quadratic Forms Over Fields written by Tsit-Yuen Lam and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Forms, Quadratic categories.
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.