Realization of arbitrary Lie algebras by automorphisms

M. A. Stepanova

Izvestiya. Mathematics , Tome 88 (2024) no. 2, pp. 313-338.

Résumé

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 $\mathfrak{h}$.

Détail

Keywords: $\mathrm{CR}$ manifold, holomorphic automorphisms, Lie algebra, symmetries of partial differential equations.

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