DEKOMPOSISI LEVI ALJABAR LIE AFFINE FROBENIUS aff(2, R)
DOI:
https://doi.org/10.25077/jmu.10.3.229-235.2021Abstract
Dalam artikel ini dipelajari aljabar Lie affine Frobenius aff(2, R) berdimensi 6. Aljabar Lie aff(2, R) dapat didekomposisi menggunakan dekomposisi Levi menjadi aljabar Lie linear khusus semisederhana sl(2, R) berdimensi 3, subaljabar Lie komutatif R ⊂ R2 berdimensi 2, dan split torus T berdimensi 1 sedemikian sehingga aff(2, R) = sl(2, R) ⊕ R ⊕ T. Karena aljabar Lie sl(2, R) semisederhana maka bracket Lie-nya dapat dinyatakan sebagai [sl(2, R), sl(2, R)] = sl(2, R). Selanjutnya, misalkan g = R⊕T sehingga aff(2, R) = sl(2, R) ⊕ g. Diperoleh bahwa [sl(2, R), g] ⊆ g dan [g, g] ⊆ g. Dalam hal ini, g adalah solvable radical dari aff(2, R).
Kata Kunci: Aljabar Lie affine, Aljabar Lie Semisederhana, Dekomposisi Levi
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