AN EXACT SYMPLECTIC STRUCTURE OF LOW DIMENSIONAL 2-STEP SOLVABLE LIE ALGEBRAS

Edi Kurniadi (Department of Mathematics of FMIPA of Universitas Padjadjaran)
Kankan Parmikanti (Departemen Matematika FMIPA Unpad)
Badrulfalah (Departemen Matematika FMIPA Unpad)

Edumatsains
Vol 8 No 2 (2024): Januari

In this paper, we study a Lie algebra equipped by an exact symplectic structure. This condition implies that the Lie algebra has even dimension. The research aims to identify and to contruct 2-step solvable exact symplectic Lie algebras of low dimension with explicit formulas for their one-forms and symplectic forms. For case of four-dimensional, we found that only one class among three classes is 2-step solvable exact symplectic Lie algebra. Furthermore, we also give more examples for case six and eight dimensional of Lie algebras with exact symplectic forms which is included 2-step solvable exact sympletic Lie algebras. Moreover, it is well known that a 2-step solvable Lie algebra equipped by an exact symplectic form is nothing but it is called a 2-step solvable Frobenius Lie algebra.