Title: The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra Show Chinese title

Title: 双洗牌李代数嵌入到Kashiwara-Vergne李代数中

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 ${\frak{grt}}\rightarrow{\frak{krv}}$. Show Chinese abstract

Abstract: 本文证明了存在一个从双洗牌李代数 ${\frak{ds}}$ 到卡西拉-韦格内李代数 ${\frak{krv}}$ 的单射李同态，与已知的格罗滕迪克-泰希米勒李代数 ${\frak{grt}}\rightarrow {\frak{ds}}$ 和 ${\frak{grt}}\rightarrow{\frak{krv}}$ 的李同态构成一个交换三角形。