Open AccessQuasi-Associative Algebras on the Frobenius Lie Algebra M_3 (R)⊕gl_3 (R)
Author(s) -
Henti Henti,
Edi Kurniadi,
Ema Carnia
Publication year - 2021
Publication title -
al-jabar
Language(s) - English
Resource type - Journals
eISSN - 2540-7562
pISSN - 2086-5872
DOI - 10.24042/ajpm.v12i1.8485
Subject(s) - associative property , mathematics , frobenius algebra , universal enveloping algebra , algebra over a field , associative algebra , pure mathematics , non associative algebra , symplectic geometry , lie algebra , dimension (graph theory) , algebra representation , division algebra
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.