Relating depth graded and block graded motivic Lie algebras

TL;DR

This paper explores the relationship between depth and block filtrations in motivic Lie algebras, providing explicit mappings and insights into their structural differences and connections to conjectures.

Contribution

It constructs an explicit dictionary linking block graded and depth graded motivic multiple zeta values, advancing understanding of their algebraic relations.

Findings

Established a correspondence between certain subspaces of block graded and totally odd multiple zeta values.

Showed that all expected relations in the depth graded motivic Lie algebra are realizable in the block graded Lie algebra.

Discussed potential implications for the Broadhurst-Kreimer conjecture.

Abstract

Using the block filtration as a realisation of the coradical filtration, we study the discrepancy between the depth filtration and the coradical filtration for motivic multiple zeta values. We construct an explicit dictionary between a certain subspace of block graded multiple zeta values and totally odd multiple zeta values and show that all expected relations in the depth graded motivic Lie algebra may be realised in the block graded Lie algebra as the kernel of an explicit map. We also discuss some connections to the uneven Broadhurst-Kreimer conjecture, and outline a possible approach.