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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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2009] ©2006 |
Year of Publication: | 2009 |
Edition: | Course Book |
Language: | English |
Series: | Mathematical Notes ;
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Physical Description: | 1 online resource (144 p.) :; 1 line illus. |
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Weiss, Richard M., author. aut http://id.loc.gov/vocabulary/relators/aut Quadrangular Algebras. (MN-46) / Richard M. Weiss. Course Book Princeton, NJ : Princeton University Press, [2009] ©2006 1 online resource (144 p.) : 1 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Notes ; 46 Frontmatter -- Contents -- Preface -- Chapter One. Basic Definitions -- Chapter Two. Quadratic Forms -- Chapter Three. Quadrangular Algebras -- Chapter Four. Proper Quadrangular Algebras -- Chapter Five. Special Quadrangular Algebras -- Chapter Six. Regular Quadrangular Algebras -- Chapter Seven. Defective Quadrangular Algebras -- Chapter Eight. Isotopes -- Chapter Nine. Improper Quadrangular Algebras -- Chapter Ten. Existence -- Chapter Eleven. Moufang Quadrangles -- Chapter Twelve. The Structure Group -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Algebra. Forms, Quadratic. MATHEMATICS Algebra General. MATHEMATICS Number Theory. MATHEMATICS / Algebra / General. bisacsh Algebra over a field. Algebraic group. Associative property. Axiom. Classical group. Clifford algebra. Commutator. Defective matrix. Division algebra. Fiber bundle. Geometry. Isotropic quadratic form. Jacques Tits. Jordan algebra. Moufang. Non-associative algebra. Polygon. Precalculus. Projective plane. Quadratic form. Simple Lie group. Subgroup. Theorem. Vector space. Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 9783110494921 ZDB-23-PMN Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691124605 https://doi.org/10.1515/9781400826940 https://www.degruyter.com/isbn/9781400826940 Cover https://www.degruyter.com/document/cover/isbn/9781400826940/original |
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English |
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Weiss, Richard M., Weiss, Richard M., |
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Weiss, Richard M., Weiss, Richard M., Quadrangular Algebras. (MN-46) / Mathematical Notes ; Frontmatter -- Contents -- Preface -- Chapter One. Basic Definitions -- Chapter Two. Quadratic Forms -- Chapter Three. Quadrangular Algebras -- Chapter Four. Proper Quadrangular Algebras -- Chapter Five. Special Quadrangular Algebras -- Chapter Six. Regular Quadrangular Algebras -- Chapter Seven. Defective Quadrangular Algebras -- Chapter Eight. Isotopes -- Chapter Nine. Improper Quadrangular Algebras -- Chapter Ten. Existence -- Chapter Eleven. Moufang Quadrangles -- Chapter Twelve. The Structure Group -- Bibliography -- Index |
author_facet |
Weiss, Richard M., Weiss, Richard M., |
author_variant |
r m w rm rmw r m w rm rmw |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Weiss, Richard M., |
title |
Quadrangular Algebras. (MN-46) / |
title_full |
Quadrangular Algebras. (MN-46) / Richard M. Weiss. |
title_fullStr |
Quadrangular Algebras. (MN-46) / Richard M. Weiss. |
title_full_unstemmed |
Quadrangular Algebras. (MN-46) / Richard M. Weiss. |
title_auth |
Quadrangular Algebras. (MN-46) / |
title_alt |
Frontmatter -- Contents -- Preface -- Chapter One. Basic Definitions -- Chapter Two. Quadratic Forms -- Chapter Three. Quadrangular Algebras -- Chapter Four. Proper Quadrangular Algebras -- Chapter Five. Special Quadrangular Algebras -- Chapter Six. Regular Quadrangular Algebras -- Chapter Seven. Defective Quadrangular Algebras -- Chapter Eight. Isotopes -- Chapter Nine. Improper Quadrangular Algebras -- Chapter Ten. Existence -- Chapter Eleven. Moufang Quadrangles -- Chapter Twelve. The Structure Group -- Bibliography -- Index |
title_new |
Quadrangular Algebras. (MN-46) / |
title_sort |
quadrangular algebras. (mn-46) / |
series |
Mathematical Notes ; |
series2 |
Mathematical Notes ; |
publisher |
Princeton University Press, |
publishDate |
2009 |
physical |
1 online resource (144 p.) : 1 line illus. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Chapter One. Basic Definitions -- Chapter Two. Quadratic Forms -- Chapter Three. Quadrangular Algebras -- Chapter Four. Proper Quadrangular Algebras -- Chapter Five. Special Quadrangular Algebras -- Chapter Six. Regular Quadrangular Algebras -- Chapter Seven. Defective Quadrangular Algebras -- Chapter Eight. Isotopes -- Chapter Nine. Improper Quadrangular Algebras -- Chapter Ten. Existence -- Chapter Eleven. Moufang Quadrangles -- Chapter Twelve. The Structure Group -- Bibliography -- Index |
isbn |
9781400826940 9783110494921 9783110442502 9780691124605 |
genre_facet |
Algebra General. Number Theory. |
url |
https://doi.org/10.1515/9781400826940 https://www.degruyter.com/isbn/9781400826940 https://www.degruyter.com/document/cover/isbn/9781400826940/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.74 |
dewey-sort |
3512.74 |
dewey-raw |
512.74 |
dewey-search |
512.74 |
doi_str_mv |
10.1515/9781400826940 |
oclc_num |
979592495 |
work_keys_str_mv |
AT weissrichardm quadrangularalgebrasmn46 |
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n |
ids_txt_mv |
(DE-B1597)446487 (OCoLC)979592495 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
Quadrangular Algebras. (MN-46) / |
container_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 |
_version_ |
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