Quadrangular Algebras. (MN-46) /

Quadrangular Algebras. (MN-46) / / Richard M. Weiss.

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 quadrangle...

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Superior document:Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016
VerfasserIn:
Weiss, Richard M.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2009]
©2006
Year of Publication:2009
Edition:Course Book
Language:English
Series:Mathematical Notes ; 46
Online Access:
Physical Description:1 online resource (144 p.) :; 1 line illus.
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245 1 0 |a Quadrangular Algebras. (MN-46) /  |c Richard M. Weiss. 
250 |a Course Book 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2009] 
264 4 |c ©2006 
300 |a 1 online resource (144 p.) :  |b 1 line illus. 
336 |a text  |b txt  |2 rdacontent 
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490 0 |a Mathematical Notes ;  |v 46 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Chapter One. Basic Definitions --   |t Chapter Two. Quadratic Forms --   |t Chapter Three. Quadrangular Algebras --   |t Chapter Four. Proper Quadrangular Algebras --   |t Chapter Five. Special Quadrangular Algebras --   |t Chapter Six. Regular Quadrangular Algebras --   |t Chapter Seven. Defective Quadrangular Algebras --   |t Chapter Eight. Isotopes --   |t Chapter Nine. Improper Quadrangular Algebras --   |t Chapter Ten. Existence --   |t Chapter Eleven. Moufang Quadrangles --   |t Chapter Twelve. The Structure Group --   |t Bibliography --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Algebra. 
650 0 |a Forms, Quadratic. 
650 0 |a MATHEMATICS  |v Algebra  |v General. 
650 0 |a MATHEMATICS  |v Number Theory. 
650 7 |a MATHEMATICS / Algebra / General.  |2 bisacsh 
653 |a Algebra over a field. 
653 |a Algebraic group. 
653 |a Associative property. 
653 |a Axiom. 
653 |a Classical group. 
653 |a Clifford algebra. 
653 |a Commutator. 
653 |a Defective matrix. 
653 |a Division algebra. 
653 |a Fiber bundle. 
653 |a Geometry. 
653 |a Isotropic quadratic form. 
653 |a Jacques Tits. 
653 |a Jordan algebra. 
653 |a Moufang. 
653 |a Non-associative algebra. 
653 |a Polygon. 
653 |a Precalculus. 
653 |a Projective plane. 
653 |a Quadratic form. 
653 |a Simple Lie group. 
653 |a Subgroup. 
653 |a Theorem. 
653 |a Vector space. 
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773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Backlist 2000-2013  |z 9783110442502 
776 0 |c print  |z 9780691124605 
856 4 0 |u https://doi.org/10.1515/9781400826940 
856 4 0 |u https://www.degruyter.com/isbn/9781400826940 
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