Bases efetivas para superbimódulos metabelianos em variedades de álgebras não associativas
The problem of the description of an effective base for some algebra A over a field F is to find a base B for the vector space A over F with a certain algorithm of multiplication of the elements from B that in consequence can be applied for computing any product in A. In the present work, we deve...
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| Formato: | Dissertação |
| Idioma: | pt_BR |
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Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/32823 |
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| Resumo: | The problem of the description of an effective base for some algebra A over a field F is
to find a base B for the vector space A over F with a certain algorithm of multiplication
of the elements from B that in consequence can be applied for computing any product
in A. In the present work, we develop some techniques of finding effective bases for Usuperbimodules of free V-birepresentations, where V runs some list of varieties of nearly
associative algebras over a field F of characteristic distinct from 2 and U runs the set of
all V-superalgebras with null multiplication. There are three levels of our study. First, we
consider cases of classical varieties of alternative (Alt), Jordan (Jord), and Malcev (Malc)
algebras. The results obtained at this level, having the form of new unpublished ones, in
fact, accumulate the experience of certain known published examples of metabelian (twostep solvable) superalgebras and known bases for subspaces of multilinear polynomials in
the free algebras of Alt, Jord, and Malc. At its second level, the study deals with the case of
the variety of all Lie-admissible algebras together with its proper subvarieties of flexible
algebras, antiflexible algebras, and the algebras with the identity of Jacobian type for
the associator function. The Theorems obtained at this level are new unpublished results
giving the explicit descriptions of bases for U-superbimodules with no restrictions on sets
of generators for U. At the third level, we apply the techniques developed throughout the
work for a finding of complete bases for the free superalgebras in certain nearly associative
varieties that are also nearly nilpotent. The results of the work can be applied to further
studies on open problems related to free superalgebras. |
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