Let 𝐿 be a free metabelian Lie algebra of finite rank at least 2. We show the existence of non-trivial fixed points of an $IA$-endomorphism of 𝐿 and give an algorithm detecting them. In particular, we prove that the fixed point subalgebra Fix 𝜑 of an $IA$-endomorphism 𝜑 of 𝐿 is not finitely generated.
Volume 130, 2020
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