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All Journal Edumatsains BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) BERNAS: Jurnal Pengabdian Kepada Masyarakat
Edi Kurniadi
Department of Mathematics of FMIPA of Universitas Padjadjaran
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Journal : BAREKENG: Jurnal Ilmu Matematika dan Terapan

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THE NON-DEGENERACY OF THE SKEW-SYMMETRIC BILINEAR FORM OF THE FINITE DIMENSIONAL REAL FROBENIUS LIE ALGEBRA Edi Kurniadi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (429.202 KB) | DOI: 10.30598/barekengvol16iss2pp379-384

Abstract

A Frobenius Lie algebra is recognized as the Lie algebra whose stabilizer at a Frobenius functional is trivial. This condition is equivalent to the existence of a skew-symmetric bilinear form which is non-degenerate. On the other hand, the Lie algebra is Frobenius as well if its orbit on the dual vector space is open. In this paper, we study the skew-symmetric bilinear form of finite dimensional Frobenius Lie algebra corresponding to its Frobenius functional. The work aims to prove that a Lie algebra of dimension is Frobenius if and only if the -th derivation of the Frobenius functional is not equal to zero. Indeed, this condition implies that the skew-symmetric bilinear form is non-degenerate and vice versa. In addition, some properties of Frobenius functionals are obtained. Furthermore, the computations are given using the coadjoint orbits and the structure matrix. As a discussion, we can investigate these results in the algebra case whether giving rise to a left-invariant K hler structure of a Frobenius Lie group or not.
Co-Authors Badrulfalah Betty Subartini Herlina Napitupulu Kankan Parmikanti Nurul Gusriani