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Doctoral Thesis
DOI
10.11606/T.45.2010.tde-16042010-133822
Document
Author
Full name
Cristina Spohr
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Grichkov, Alexandre (President)
Ananin, Alexandre
Giuliani, Maria de Lourdes Merlini
Guzzo Junior, Henrique
Zubkov, Alexandr
Title in Portuguese
Loops de Bol 2-nilpotentes e de expoente 2
Keywords in Portuguese
álgebra alternativa à direita
álgebra de loop
loops 2-nilpotentes
Loops de Bol
loops de expoente 2
Abstract in Portuguese
Neste trabalho estudamos loops de Bol 2-nilpotentes e de expoente 2. Além disso, mostramos que o ideal de aumento de uma álgebra de loop, de um loop finito p-nilpotente em característica p > 0, é nilpotente. Com este resultado conseguimos caracterizar os elementos inversíveis da álgebra de loop de um loop 2-nilpotente sobre um corpo de dois elementos. Provamos também que loops de Bol finitos 2-nilpotentes e de expoente 2 podem ser mergulhados em um loop de Bol à direita de elementos inversíveis de uma álgebra alternativa à direita, sobre um corpo de característica dois.
Title in English
2-nilpotent Bol loops of exponent 2
Keywords in English
2-nilpotent loops
Bol loops
loop algebra
loops of exponent 2
right alternative algebra.
Abstract in English
In this work we study 2-nilpotent Bol loops of exponent 2. Besides, we prove that the augmentation ideal of a loop algebra, of a finite p-nilpotent loop in characteristic p > 0, is nilpotent. With this result we characterized the invertible elements of the loop algebra of a 2-nilpotent loop over a field with two elements. We also proof that 2-nilpotent Bol loops of exponent 2 may be embedded into a right Bol loop of invertible elements of a right alternative algebra, over a field of characteristic 2.
 
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capacris.pdf (42.54 Kbytes)
lbnilp2_grishk.pdf (367.33 Kbytes)
Publishing Date
2010-10-27
 
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