Open AccessOn Frobenius functionals of the Lie algebra M3(ℝ) ⊕ gl3(ℝ)
Author(s) -
Henti,
Edi Kurniadi,
Ema Carnia
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1872/1/012015
Subject(s) - mathematics , lie conformal algebra , graded lie algebra , algebra over a field , pure mathematics , universal enveloping algebra , vector space , lie algebra , dimension (graph theory) , frobenius theorem (differential topology) , geometry , scalar curvature , curvature , ricci flat manifold
In the present paper, we study the Lie algebra written in the semi-direct sum formula of the vector space M 3 (ℝ) and the Lie algebra gl 3 (ℝ) whose both contain 3×3 real matrices. We denote it by g 3 : = M 3 (ℝ) ⊕ gl 3 (ℝ). The aim of this research is to study the existence of a linear functional such that g 3 is the Frobenius Lie algebra of dimension 18. Such the linear functional is called the Frobenius functional. We applied the literature reviews to achieve this result, particularly we study the notion of Frobenius Lie algebra in Ooms and Rais results. The main result of our research is the proof that g 3 is Frobenius Lie algebra. For the future research, the existence of a Frobenius functional is still an open problem to study for higher dimensional Lie algebras.