A Basis For The Relative Lie Algebra Of Brunnian Braids

Brunnian braids have interesting relations with homotopy groups of spheres.In this paper,we investigate the Lie algebra of the descending central series related to subgroup of the pure group.In order to determine the basis for the relative Lie algebra L^P（Brun_n）,we study the relationship ofL^P（Brun_n）andL^Fn-1（Brun_n）.With the help of the Hall basis of free Lie algebra L(F_n-1),the basis of relative Lie algebra L^P（Brun_n）is given.