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Master's Dissertation
DOI
10.11606/D.45.1998.tde-01092009-171526
Document
Author
Full name
Fernando Martins Antoneli Junior
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1998
Supervisor
Committee
Forger, Frank Michael (President)
Hornos, Jose Eduardo Martinho
Sidki, Said Najati
Title in Portuguese
Subalgebras maximais das álgebras de Lie semisimples, quebra de simetria e o código genético
Keywords in Portuguese
Grupos e Álgebras de Lie
Quebra de Simetria
Abstract in Portuguese
O propósito deste trabalho é dar uma contribuição ao projeto iniciado por Hornos & Hornos que visa explicar as degenerescências do código genético como resultado de sucessivas quebras de simetria ocorridas durante sua evolução. O modelo matemático usado requer a construção de todas as representações irredutíveis de dimensão 64 das álgebras de Lie simples (chamadas representações de códons) e a análise de suas regras de ramicação sob redução a subalgebras. A classicação de todas as possibilidades é baseada na classicação das subalgebras maximais das álgebras de Lie semisimples obtida por Dynkin. No presente trabalho, os resultados de Dynkin são apresentados em linguagem e notação moderna e são aplicados ao problema de construir todas as possíveis cadeias de subalgebras maximais das álgebras de Lie simples B_6 = so(13) e D_7 = so(14) e de identicar aquelas que reproduzem as degenerescências do código genético.
Title in English
Maximal Sub-algebras of Semi-simple Lie Algebras, Symmetry Breaking and the Genetic Code
Keywords in English
Evolution of the Genetic Code
Lie Groups and Algebras
Symmetry Breaking
Abstract in English
The purpose of this work is to make a contribution to the project initiated by Hornos & Hornos which aims at explaining the degeneracy of the genetic code as the result of a sequence of symmetry breaking that occurred during its evolution. The mathematical model employed requires the construction of all 64-dimensional irreducible representations of simple Lie algebras (called codon representations) and the analysis of their branching rules under reduction to sub-algebras. The classification of all possibilities is based on Dynkins classification of the maximal sub-algebras of semi-simple Lie algebras. In the present work, Dynkins results are presented in modern language and notation and are applied to the problem of constructing all possible chains of maximal sub-algebras of the simple Lie algebras B_6 = so(13) and D_7 = so(14) and of identifying all those that reproduce the degeneracies of the genetic code.
 
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antonelijrMS.pdf (636.83 Kbytes)
Publishing Date
2009-10-07
 
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