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Doctoral Thesis
DOI
Document
Author
Full name
Fernando Henry Meirelles
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2014
Supervisor
Committee
Chestakov, Ivan (President)
Kochloukov, Plamen Emilov
Kornev, Alexandr
Murakami, Lucia Satie Ikemoto
Sviridova, Irina
Title in Portuguese
Identidades polinomiais da álgebra de octônios
Keywords in Portuguese
Álgebra alternativa
Álgebra de malcev
Identidade polinomial
Superálgebra
Abstract in Portuguese
Neste trabalho encontramos bases para as identidades T Z 32 e T Z 22 gradu- adas dos octônios. Utilizando a base obtida no T Z 22 , re-obtivemos uma base para as identidades Z 2 -graduadas das matrizes dois por dois. Também obti- vemos as identidades simultaneamente fracas e antissimétricas ou skew dos octônios na categorias de álgebras alternativas. Também obtivemos as identi- dades antissimétricas da álgebra de Malcev simples de dimensão sete, sl(O). Para ambos os casos estudados de identidades não graduadas dos octônios, mostramos positivamente a conjectura de Shestakov-Zhukavets: O T -ideal de identidades dos octônios coincide com o da álgebra alternativa quadrá- tica.
Title in English
Polynomial identities of the octonion algebra
Keywords in English
Alternative algebra
Malcev algebra
Polynomial identity
Superalgebra
Abstract in English
In this work we find bases for the T Z 32 and T Z 22 graded identities of the octonion algebra. Using the base obtained in the T Z 22 case, we re-obtain a basis for the Z 2 -graded identities of two by two matrices. We also obtained the simultaneously skew and weak identities of the octonions in the category of alternative algebras. In addition we find a basis of identities for the simple Malcev algebra of dimension seven, sl(O). For both skew cases of identities studied we positively show the Shestakov-Zhukavets conjecture: The T -ideal of identities of the octonions coincides with that of the quadratic alternative algebra.
 
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Publishing Date
2019-09-25
 
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