Abstract
Let be a finite-dimensional complex Lie algebra and be the affine variety of all multiplicative Hom-Lie algebras on . We use a method of computational ideal theory to describe , showing that consists of two 1-dimensional and one 3-dimensional irreducible components and for . We construct a new family of multiplicative Hom-Lie algebras on the Heisenberg Lie algebra and characterize the affine varieties and . We also study the derivation algebra of a multiplicative Hom-Lie algebra D on and, under some hypotheses on D, we prove that the Hilbert series is a rational function.
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