[04/10/2024] N. Confurius - On Hoffman's basis conjecture for formal multiple zeta values скачать в хорошем качестве

[04/10/2024] N. Confurius - On Hoffman's basis conjecture for formal multiple zeta values

Multiple zeta values (MZV's) are real numbers that appear in various areas of mathematics and physics. A conjecture from 1997 by M. Hoffman proposes an explicit basis for the space of MZV's over the rationals. In 2012, F. Brown proved an analogue of this conjecture for motivic MZV's. His theorem implies that Hoffman's conjectural basis is a spanning set for MZV's, while the linear independence of this set remains an open question. Formal MZV's allow us to study MZV's by algebraic methods in a way that cimcumvents transcendence issues. The theory of post-Lie algebras allows for a convenient approach to recover a coaction on the algebra of formal MZV's. We then revisit Brown's proof in this context and obtain a conditional result. We show that Hoffman's conjecture for formal MZV's is implied by a well-known conjecture on the algebraic structure of the double shuffle Lie algebra.