• Fixed Points of $IA$-Endomorphisms of a Free Metabelian Lie Algebra

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/121/04/0405-0416

• Keywords

Free metabelian Lie algebra; fixed point.

• Abstract

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.

• Author Affiliations

1. Department of Mathematics, Çukurova University, Adana, Turkey
2. Department of Mathematics, Melikşah University, Kayseri, Turkey

• Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

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Posted on July 25, 2019