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Documents  Elduque, Alberto | enregistrements trouvés : 2

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Triality Elduque, Alberto | CIRM H

Post-edited

Research talks;Algebra

Duality in projective geometry is a well-known phenomenon in any dimension. On the other hand, geometric triality deals with points and spaces of two different kinds in a sevendimensional projective space. It goes back to Study (1913) and Cartan (1925), and was soon realizedthat this phenomenon is tightly related to the algebra of octonions, and the order 3 outer automorphisms of the spin group in dimension 8.
Tits observed, in 1959, the existence of two different types of geometric triality. One of them is related to the octonions, but the other one is better explained in terms of a class of nonunital composition algebras discovered by the physicist Okubo (1978) inside 3x3-matrices, and which has led to the definition of the so called symmetric composition algebras.
This talk will review the history, classification, and their connections with the phenomenon of triality, of the symmetric composition algebras.
Duality in projective geometry is a well-known phenomenon in any dimension. On the other hand, geometric triality deals with points and spaces of two different kinds in a sevendimensional projective space. It goes back to Study (1913) and Cartan (1925), and was soon realizedthat this phenomenon is tightly related to the algebra of octonions, and the order 3 outer automorphisms of the spin group in dimension 8.
Tits observed, in 1959, the ...

17A75 ; 20G15 ; 17B60

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- xiii; 336 p.
ISBN 978-0-8218-9846-8

Mathematical surveys and monographs , 0189

Localisation : Collection 1er étage

algèbre graduée # algèbre de Lie # décomposition de Cartan # classification

17B70 ; 17B60 ; 16W50 ; 17A75 ; 17C50 ; 17-02

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