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Doctoral Thesis
DOI
Document
Author
Full name
Celi Vasques Crepaldi
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1986
Supervisor
Committee
Dias, Candido Lima Silva (President)
Conde, Antonio
Manzoli Neto, Oziride
Qualifik, Paul
Teixeira, Mario Tourasse
Title in Portuguese
A ÁLGEBRA DE CLIFFORD CANÔNICA
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
Not available
Keywords in English
Not available
Abstract in English
Our intention was to construct and study one Clifford algebra CM, which has a fundamental importance to the determination of other Clifford al gebras. Moreover, it allows the stablishment of the relation between the Clifford algebra of vector space E, of a finite dimension, and the exterior algebra of that space: ΛE. The algebra CM is a Clifford algebra of the space M = E ⊕ E8, which the quadratic form Q((x,x')) = <x, x'>. When we have studied the properties of this algebra, we have come to the conclusion that the quadratic space M (and the space E) over the field K, has an inner product. The orthogonal group G de CM and the Clifford group de G are very important and have been described and analysed in Chapter IL. In Chapter III, we have construct one algebra on the vector space E with a quadratic form Q, induced from Q, and by analogy, we have construct one algebra on the vector space E*, we have also stablished the relations among the algebras CM, CE e CE*. On Chapter IV, we have shown that the Clifford algebra of E can be obtained as a deformation of the exterior algebra *Lambda;E, based.on the works of J. Helmstetter and using the interior products. Finally, we have shown an analogy between the reasoning of Helmstetter and the results we have attained.
 
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Publishing Date
2019-11-29
 
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