Depth-graded motivic Lie algebra

Abstract

In this paper we suggest a way to understand the structure of depth-graded motivic Lie subalgebra generated by the depth one part for the neutral Tannakian category mixed Tate motives over Z. We will show that from an isomorphism conjecture proposed by K. Tasaka we can deduce the F. Brown's matrix conjecture and the nondegeneracy conjecture about depth-graded motivic Lie subalgebra generated by the depth one part.