Quasi-Associative Algebras on the Frobenius Lie Algebra M_3 (R)⊕gl_3 (R)

Henti Henti, Edi Kurniadi, Ema Carnia


In this paper, we study the quasi-associative algebra property for the real Frobenius  Lie algebra  of dimension 18. The work aims  to prove that  is a quasi-associative algebra and to compute its formulas explicitly. To achieve this aim, we apply the literature reviews method corresponding to Frobenius Lie algebras, Frobenius functionals, and the structures of quasi-associative algebras. In the first step, we choose a Frobenius functional determined by direct computations of a bracket matrix of  and in the second step, using an induced symplectic structure, we obtain the explicit formulas of quasi-associative algebras for . As the results, we proved that  has the quasi-associative algebras property, and we gave their formulas explicitly. For future research, the case of the quasi-associative algebras on   is still an open problem to be investigated. Our result can motivate to solve this problem. 



Frobenius Lie Algebras; Frobenius Functionals; Quasi- Associative Algebras; Symplectic Structures.

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DOI: http://dx.doi.org/10.24042/ajpm.v12i1.8485


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