On Power-Associative Nilalgebras of Dimension N and Nilindex N-1 |
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| Authors: | Juan C Gutierrez Fernandez Claudia I Garcia José Ignacio Martinez M L R Montoya |
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| Institution: | 1. Departamento de Matemática e Estatística , Universidade de S?o Paulo , S?o Paulo , Brazil jcgf@ime.usp.br;3. Escola de Artes, Cie^ncias e Humanidades, EACH , Universidade de S?o Paulo , S?o Paulo , Brazil;4. ETS de Ingenieria Informática , Universidad Rey Juan Carlos , Madrid , Spain;5. Instituto de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia , Medellín , Colombia |
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| Abstract: | Whether or not a finite-dimensional, commutative, power-associative nilalgebra is solvable is a well-known open problem. In this paper, we describe commutative, power-associative nilalgebras of dimension n ≥ 6 and nilindex n ? 1 based on the condition that n ? 4 ≤ dim 𝔄3 ≤ n ? 3. This paper is a continuation of 10
Fernadez , J. C. G. ,
Garcia , C. I. ,
Montoya , M. L. R. ( 2013 ). On power-associative nilalgebras of nilindex and dimension n . Revista Colombiana de Matemáticas 47 : 1 – 11 . Google Scholar]], where we describe commutative power-associative nilalgebras of dimension and nilindex n. We observe that the Jordan case was obtained by L. Elgueta and A. Suazo in 2
Elgueta , L. ,
Suazo , A. ( 2002 ). Jordan nilalgebras of nilindex n and dimension n + 1 . Comm. Algebra 30 : 5547 – 5561 .Taylor &; Francis Online], Web of Science ®] , Google Scholar]]. |
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| Keywords: | Commutative Nilalgebra Power-associative algebra |
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