Quasi-Associative Algebras on the Frobenius Lie Algebra M_3 (R)⊕gl_3 (R) - Henti, Henti; Kurniadi, Edi; Carnia, Ema (Universitas Islam Raden Intan Lampung, INDONESIA, 2021)
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.