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All Journal EKSAKTA: Journal of Sciences and Data Analysis Epsilon: Jurnal Matematika Murni dan Terapan CAUCHY: Jurnal Matematika Murni dan Aplikasi Edumatsains Jurnal Matematika: MANTIK JMPM: Jurnal Matematika dan Pendidikan Matematika Teorema: Teori dan Riset Matematika Jurnal Cendekia : Jurnal Pendidikan Matematika Jambura Journal of Mathematics ComTech: Computer, Mathematics and Engineering Applications Jurnal Matematika UNAND Kumawula: Jurnal Pengabdian Kepada Masyarakat JURNAL PENDIDIKAN MIPA BERNAS: Jurnal Pengabdian Kepada Masyarakat Seminar Nasional Hasil Riset dan Pengabdian (SNHRP) Jurnal Matematika Integratif Mathematical Sciences and Applications Journal
Edi Kurniadi
Departemen Matematika, FMIPA, Universitas Padjadjaran
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Journal : Edumatsains

 1 
KILLING FORM ALJABAR LIE FROBENIUS BERDIMENSI ≤4 UNTUK MENENTUKAN KESEMISEDERHANAANNYA Edi Kurniadi
EduMatSains : Jurnal Pendidikan, Matematika dan Sains Vol 6 No 1 (2021): Juli
Publisher : Fakultas Keguruan dan Ilmu Pendidikan, Universitas Kristen Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33541/edumatsains.v6i1.2999

Abstract

We study the notion of the Killing form for Frobenius Lie algebras of dimension . The Killing form is a symmetric bilinear form on a finite dimensional Lie algebra over a field defined by where is denoted the trace and is an adjoint representation of . A Lie algebras is said to be semisimple if it has the nondegenerate Killing form. The research aims to consider the criterion for semisimplicity of Frobenius Lie algebras of dimension by using the Killing form. The results show that each Frobenius Lie algebra of dimension and is not semisimple since the the Killing form is degenerate or in other words, a determinant of a representation matrix of the Killing form is equal to zero. For the future research, it is still an open problem to consider the general formulas of the Killing form for higher dimensional Frobenius Lie algebra whether degenerate or nondegenerate such that the semisimplicity of a Lie algebra can be considered. We conjecture that each finite dimensional real Frobenius Lie algebra is not semisimple.
AN EXACT SYMPLECTIC STRUCTURE OF LOW DIMENSIONAL 2-STEP SOLVABLE LIE ALGEBRAS Edi Kurniadi; Kankan Parmikanti; Badrulfalah
EduMatSains : Jurnal Pendidikan, Matematika dan Sains Vol 8 No 2 (2024): Januari
Publisher : Fakultas Keguruan dan Ilmu Pendidikan, Universitas Kristen Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33541/edumatsains.v8i2.5319

Abstract

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.
Co-Authors Alit Kartiwa Asep Supriatna Badrulfalah Badrulfalah Betty Subartini Diah Ayu Pratiwi Dody Jesaya Sinaga Ema Carnia Endang Rusyaman Henti Henti Henti Henti Herlina Napitupulu Isah Aisah Kankan Parmikanti Laily Wadil Muqadas Mohamad Nurzaman Muhammad Zaky Zachary Nurul Gusriani Putri Giza Maharani Riaman Riaman Sisilia Sylviani Stanley P. Dewanto