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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.1998.tde-20210813-161705
Document
Author
Full name
Walquiria de Freitas Torezani
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1998
Supervisor
Title in Portuguese
Álgebras com composição e álgebras com pseudo-composição
Keywords in Portuguese
Álgebra
Anéis e Álgebras Não Associativos
Abstract in Portuguese
Este trabalho resultou do estudo do artigo Pseudo-composition algebras de K.Meyberg e J.M.Osborn. No Capítulo 1, classificamos as álgebras com composição. Mostramos que estas álgebras tem dimensão 1,2,4 e 8 e são isomorfas, respectivamente, a um corpo, à álgebra de complexos generalizada, à álgebra dos quatérnios generalizada e à álgebra de Cayley-Dickson. No capítulo 2, caracterizamos as álgebras com pseudo-composição sobre um corpo algebricamente fechado. Mostramos que estas álgebras ou são do tipo quadrático, ou módulo o radiacal de sua forma bilinear são do tipo quadrático, ou podem ser construídas a partir de uma álgebra alternativa quadrática com composição
Title in English
not available
Abstract in English
This work is based on the paper Pseudo-composition algebras by K.Meyberg e J.M. Osborn. In the first chapter we classify the composition algebras. The main result establishes that these algebras have dimension 1, 2, 4 and 8, and are isomorphic, respectively, to a field, an algebras of generalized complex numbers, a generalized quaternion algebra and a Cayley-Dickson algebra. In the second chapter we characterize the pseudo-compositions algebras over an algebraically closed field. We proved that these algebras are either of quadratic type, or else module the radical of their bilinear forms are of quadratic type, or else the algebras may be constructed from an alternative quadratic composition algebra
 
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Publishing Date
2021-08-13
 
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