## Free Lie AlgebrasAlthough Lie polynomials first appeared at the turn of the century, there have been many recent developments especially from the point of view of representation theory. This book covers all aspects, with emphasis on the algebraic and combinatorial point of view as well as representation theory. |

### Contents

Logarithms and exponentials | 52 |

Hall bases | 84 |

Applications of Hall sets | 105 |

Copyright | |

8 other sections not shown

### Common terms and phrases

a₁ algebra homomorphism alphabet basis bijection canonical coefficient commutative concatenation conjugacy class conjugate cycle type deduce defined denote element endomorphism equal equivalent finite formula free group free Lie algebra free monoid h₁ h₂ Hall polynomials Hall set Hall trees Hall words Hence homogeneous Lie polynomials i₁ idempotent identity implies induction integers isomorphism k₁ l₁ legal rise Lemma Let H letter Lie idempotent Lie series linear combination linear mapping Lyndon word max(s Moreover multilinear multisets nonempty word obtain P₁ partition permutation polynomials of degree primitive necklaces Proof Let proof of Theorem proper right factor prove Reutenauer root of unity S₁ Section shows shuffle algebra shuffle product standard factorization standard sequence subalgebra subset subspace subword functions Suppose symmetric functions symmetric group t₁ Theorem 5.1 totally ordered u₁ unique words of length Σ Σ