An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra

Shigeyuki Morita; Takuya Sakasai; Masaaki Suzuki

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arXiv · 1608.07645

An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra

Shigeyuki Morita·Takuya Sakasai·Masaaki Suzuki

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Abstract

We construct an abelian quotient of the symplectic derivation Lie algebra $\mathfrak{h}_{g,1}$ of the free Lie algebra generated by the fundamental representation of $\mathrm{Sp}(2g,\mathbb{Q})$. More specifically, we show that the weight $12$ part of the abelianization of $\mathfrak{h}_{g,1}$ is $1$-dimensional for $g \ge 8$. The computation is done with the aid of computers.

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Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki. 2016-08-27. An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra. https://arxiv.org/abs/1608.07645

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