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arXiv · 2504.14293

The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra

Leila Schneps
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Abstract

In this article we prove that there exists an injective Lie morphism from the double shuffle Lie algebra ${\frak{ds}}$ into the Kashiwara-Vergne Lie algebra ${\frak{krv}}$, forming a commutative triangle with the known Lie injections of the Grothendieck-Teichm\"uller Lie algebra ${\frak{grt}}\rightarrow {\frak{ds}}$ and ${\frak{grt}}\rightarrow{\frak{krv}}$.

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Leila Schneps. 2025-04-19. The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra. https://arxiv.org/abs/2504.14293

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