SEPUTAR ALJABAR ENVELOPING UNIVERSAL DARI ALJABAR LIE FROBENIUS BERDIMENSI 4

Edi Kurniadi; Badrulfalah Badrulfalah; Kankan Parmikanti

doi:10.20527/epsilon.v18i2.13798

SEPUTAR ALJABAR ENVELOPING UNIVERSAL DARI ALJABAR LIE FROBENIUS BERDIMENSI 4

Edi Kurniadi, Badrulfalah Badrulfalah, Kankan Parmikanti

Abstract

Setiap aljabar Lie mempunyai aljabar enveloping universal dan bersifat tunggal. Dalam penelitian ini, dipelajari aljabar enveloping universal dari suatu aljabar Lie Frobenius berdimensi 4. Tujuannya adalah untuk membuktikan bahwa aljabar enveloping universal dari suatu aljabar Lie Frobenius berdimensi 4 bersifat primitif. Pertama-tama, dikonstruksi suatu basis untuk aljabar enveloping universal menggunakan Teorema Poincare-Birkhoff-Witt untuk menentukan secara eksplisit aljabar enveloping universalnya dan langkah kedua, menentukan karakteristik aljabar enveloping universal hasil konstruksi. Hasil dalam penelitian ini menunjukkan bahwa setiap aljabar enveloping universal dari aljabar Lie Frobenius berdimensi 4 senantiasa bersifat primitif.

Keywords

Aljabar Lie Frobenius, aljabar enveloping universal, aljabar primitif, aljabar tensor.

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References

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DOI: https://doi.org/10.20527/epsilon.v18i2.13798