Algorithmic problems for free Poisson algebras

Received: 29.VIII.2018, Accepted: 29.XI.2018

Abstract. It is well known that the ideal membership problem for free Lie algebras is undecidable which implies the undecidability of the ideal membership problem for free Poisson algebras. Using that fact we prove that  the subalgebra membership problem is algorithmically undecidable for free Poisson algebras.

Keywords: Free Poisson algebras, the ideal membership problem, the subalgebra membership problem

Mathematics Subject Classification (2010): 17B63, 12L05, 13P10

Zehra Velioğlu, Department of Mathematics, Faculty of Science, Harran University, Şanhurfa, Turkey