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.
Acknowledgements
The authors would like to thank the two referees and the editor for their helpful suggestions and comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).