The free partially commutative Lie algebra: Bases and ranks
Let \(K\) be an associative commutative ring and let \(L(A,\theta)\) be the free partially commutative Lie \(K\)-algebra over an alphabet \(A\); \(L(A,\theta)\) is the Lie algebra generated by \(A\) where the only defining relations \(\theta\) are the commutative law between some of the elements from \(A\). The main purpose of the paper under review is to show that \(L(A,\theta)\) enjoys a lot of properties of the free Lie algebra. The authors obtain a version of the Lazard elimination process, prove that \(L(A,\theta)\) is a free \(K\)-module and construct explicitly \(K\)-bases for it. They also show how the classical Witt calculus can be extended to \(L(A,\theta)\).
scientific article; zbMATH DE number 94904
scientific article