| Description |
1 online resource (v, 90 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 1947-6221 ; number 1245 |
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Memoirs of the American Mathematical Society ; no. 1245.
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| Contents |
Cover; Title page; Introduction; Organization of the paper; Acknowledgments; Chapter 1. Moufang sets; 1.1. Definitions and basic properties; 1.2. Moufang sets from linear algebraic groups; 1.3. Moufang sets from Jordan algebras; 1.4. Moufang sets from skew-hermitian forms; Chapter 2. Structurable algebras; 2.1. Definitions and basic properties; 2.2. Conjugate invertibility in structurable algebras; 2.3. Examples of structurable algebras; 2.4. Construction of Lie algebras from structurable algebras; 2.5. Isotopies of structurable algebras; Chapter 3. One-invertibility for structurable algebras |
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3.1. Algebraicity of 5-graded Lie algebras3.2. One-invertibility in \A×\Ss; 3.3. One-invertibility for structurable division algebras; Chapter 4. Simple structurable algebras and simple algebraic groups; 4.1. Simple algebraic groups from simple structurable algebras; 4.2. Deducing algebraicity; 4.3. Structurable division algebras from simple algebraic groups of -rank 1; Chapter 5. Moufang sets and structurable division algebras; 5.1. Moufang sets from structurable division algebras; 5.2. Structurable division algebras from algebraic Moufang sets; Chapter 6. Examples |
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6.1. Associative algebras with involution6.2. Jordan algebras; 6.3. Hermitian structurable algebras; 6.4. Structurable algebras of skew-dimension one; 6.5. Forms of the tensor product of two composition algebras; 6.6. Classification theorem for structurable division algebras; Bibliography; Back Cover |
| Summary |
"A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. We extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, we show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. We also obtain explicit formulas for the root groups, the tau-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups."--Abstract |
| Notes |
"May 2019 - Volume 259 - Number 1245 (second of 8 numbers)." |
| Bibliography |
Includes bibliographical references (pages 87-90) |
| Notes |
Print version record |
| Subject |
Algebra, Abstract.
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Jordan algebras.
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Lie algebras.
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Root systems (Algebra)
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Álgebras de Lie
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Álgebras de Jordan
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Álgebra abstracta
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Algebra, Abstract
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Jordan algebras
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Lie algebras
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Root systems (Algebra)
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| Form |
Electronic book
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| Author |
Medts, Tom de, 1980-
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Stavrova, Anastasia
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| LC no. |
2019023420 |
| ISBN |
1470452456 |
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9781470452452 |
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