Division pairs: a new approach to Moufang sets

Loos, Ottmar

doi:10.1515/advgeom-2015-0003

Cited by 2 publications

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“…However, it is shown in [DMS09, Lemma 4.1.2] that M(U, τ ) = M(U, µ a ) for all a ∈ U * , and in fact, the data U, (µ a ) a∈U * is uniquely determined by the Moufang set. On the other hand, see [Loo15] for a different approach to Moufang sets that avoids this issue.…”

Section: Organization Of the Papermentioning

confidence: 99%

Moufang sets and structurable division algebras

Boelaert¹,

Medts²,

Stavrova³

2016

Preprint

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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 3.1. Algebraicity of 5-graded Lie algebras 3.2. One-invertibility in A × S 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 k-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 6.1. Associative algebras with involution 6.2. 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 iii

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Section: Organization Of the Papermentioning

confidence: 99%

Moufang sets and structurable division algebras

Boelaert¹,

Medts²,

Stavrova³

2016

Preprint

View full text Add to dashboard Cite

show abstract

Moufang Sets and Structurable Division Algebras

2019

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Introduction vii Organization of the paper ix Acknowledgments x 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 3.1. Algebraicity of 5-graded Lie algebras 3.2. One-invertibility in A × S 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 k-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 6.1. Associative algebras with involution 6.2. 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

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Division pairs: a new approach to Moufang sets

Cited by 2 publications

References 6 publications

Moufang sets and structurable division algebras

Moufang sets and structurable division algebras

Moufang Sets and Structurable Division Algebras

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