# THE LEVI DECOMPOSITION OF THE LIE ALGEBRA M_2 (R)⋊gl_2 (R)

### Abstract

*The idea of the Lie algebra * * is studied in this research. The decomposition between Levi sub-algebra and the radical can be used to define the finite dimensional Lie algebra. The Levi decomposition is the name for this type of decomposition. The goal of this study is to obtain a Levi decomposition of the Lie algebra * * of dimension 8. We compute its Levi sub-algebra and the radical of Lie algebra * * with respect to its basis to achieve this goal. We use literature studies on the Levi decomposition and Lie algebra in Dagli result to produce the radical and Levi sub-algebra. It has been shown that * * can be decomposed in the terms of the Levi sub-algebra and its radical. In this resulst, it has been given by direct computations and we obtained that the explicit formula of Levi decomposition of **the affine Lie algebra * * **whose basis is * * is written by * * with is * * is the Levi sub-algebra of * *.*

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### References

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*BAREKENG: J. Math. & App.*, vol. 18, no. 2, pp. 0717-0724, May 2024.

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