Eksistensi Fungsional Frobenius dan Simplektik Linear Form Pada Aljabar Lie aff(3,R)

Edi Kurniadi; Aurillya Queency; Firdaniza Firdaniza

doi:10.29303/jm.v7i2.8906

Eksistensi Fungsional Frobenius dan Simplektik Linear Form Pada Aljabar Lie aff(3,R)

Authors

Edi Kurniadi , Aurillya Queency , Firdaniza Firdaniza

DOI:

10.29303/jm.v7i2.8906

Published:

2025-05-28

Issue:

Vol. 7 No. 2 (2025): Edisi Juni

Keywords:

Aljabar Lie Affine; Frobenius; Simplektik linear 2-form; Frobenius fungsional

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Kurniadi, E., Aurillya Queency, & Firdaniza, F. (2025). Eksistensi Fungsional Frobenius dan Simplektik Linear Form Pada Aljabar Lie aff(3,R). Mandalika Mathematics and Educations Journal, 7(2), 368–375. https://doi.org/10.29303/jm.v7i2.8906

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Abstract

Aljabar Lie dari grup Lie Aff(n,R) dinotasikan oleh aff(n,R) di mana setiap anggotanya dapat dinyatakan dalam bentuk matriks berukuran (n+1) x (n+1). Sifat Frobenius ini mengakibatkan adanya Frobenius fungsional yang bekorepondensi dengan bentuk simplektiknya. Tujuan penelitian ini adalah untuk menentukan bentuk simplektik pada aff(3,R). Pendekatan yang digunakan dalam penelitian ini adalah kombinasi dari metode kuantitatif berupa penentuan rumus eksplisit simplektik linear 2-form pada aff(3,R) dan metode kualitatif berupa studi literatur. Hasil yang diperoleh bahwa setiap Frobenius fungsional dari aljabar Lie affine senantiasa dapat dikonstruksi simplektik 2-form linear yang bersifat skew-simetrik dan non-degenerate sedemikian sehingga aljabar Lie affine aff(3,R) ini bersifat Frobenius. Hasil penelitian ini dapat dikembangkan untuk rumus umum bentuk simplektik aff(n,R), n>=4.

References

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Eksistensi Fungsional Frobenius dan Simplektik Linear Form Pada Aljabar Lie aff(3,R)

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