Geodesic
Realization of arbitrary Lie algebras by automorphisms
Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 313-338

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For any finite-dimensional real Lie algebra $\mathfrak{h}$, we construct a germ of a real analytic hypersurface in complex space such that its Lie algebra of infinitesimal holomorphic automorphisms is isomorphic to $\mathfrak{h}$. For any $\mathfrak{h}$, we also construct a system of partial differential equations whose Lie algebra of symmetries is isomorphic to the complexification of the algebra $\mathfrak{h}$.
Keywords: $\mathrm{CR}$ manifold, holomorphic automorphisms, Lie algebra, symmetries of partial differential equations. 
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     author = {M. A. Stepanova},
     title = {Realization of arbitrary {Lie} algebras by automorphisms},
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M. A. Stepanova. Realization of arbitrary Lie algebras by automorphisms. Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 313-338. http://geodesic.mathdoc.fr/item/IM2_2024_88_2_a6/