Abelian product of free Abelian and free Lie algebras

Authors : Zeynep ÖZKURT, Naime EKİCİ

Pages : 331-337

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Publication Date : 2018-04-01

Article Type : Research Paper

Abstract :Let $F_{n}$ be a free Lie Algebra of finite rank $n$ and $A$ be a free abelian Lie algebra of finite rank $m\geq 0$ . We investigate the properties of the generating sets and subalgebras of the abelian product $A\ast _{ab}F_{n}$. Moreover these properties are used to solve the membership problem for $A\ast _{ab}F_{n}$.
Keywords : Generating set, Abelian product, Free Lie Algebra