Free Partially Commutative Structures Original Research Article

In this paper, we study algebraic structures defined by a presentation of the form left angle bracket A; ab = ba for (a, b) set membership, variant image right-pointing angle bracket. We show that these relators are the only one that can be interpreted as both monoid and Lie relators. We also study the free partially commutative monoids, Lie algebras, and groups: in all of these cases, we show how to obtain decomposition results for these structures into the corresponding free structures.