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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Nurul Gusriani, Nurul
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Mathematics

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A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8 Kurniadi, Edi; Gusriani, Nurul; Subartini, Betty
CAUCHY Vol 7, No 2 (2022): CAUCHY: Jurnal Matematika Murni dan Aplikasi (May 2022) (Issue in Progress)
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i2.13462

Abstract

Let  be the Lie algebra of  the semi-direct sum of the real vector space   and the Lie algebra  of the sets of all  real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra  to be the real Frobenius Lie algebra of dimension 8. Moreover,  a bilinear form corresponding to this Frobenius functional is symplectic. Then the obtained symplectic bilinear form induces the left-symmetric algebra structures on . In other words, the Lie algebra   is the left-symmetric algebra. In particular, we give the formulas of its left-symmetric algebra structure explicitely. The left-symmetric algebra structures for case of higher dimension of this Lie algebra type are still an open problem to be investigated.
Co-Authors Anita Triska, Anita Betty Subartini Edi Kurniadi Kankan Parmikanti Tiara Aprilia K, Tiara