Cauchy: Jurnal Matematika Murni dan Aplikasi (Mar 2022)

A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8

  • Edi Kurniadi,
  • Nurul Gusriani,
  • Betty Subartini

DOI
https://doi.org/10.18860/ca.v7i2.13462
Journal volume & issue
Vol. 7, no. 2
pp. 267 – 280

Abstract

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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.

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