Lie algebras of Galois representations on fundamental groups

Abstract

In this paper we are studying Lie algebras associated with Galois representations on the fundamental groups of $\mathbb{P}^1_{\bar{\mathbb{Q}}} \setminus ( \{0,\infty\} \cup \mu_{2^n})$ and $\mathbb{P}^1_{\bar{\mathbb{Q}}} \setminus ( \{0,\infty\} \cup \mu_{3^n})$.