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ABSTRACT
We construct an abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra generated by the fundamental representation of
. More specifically, we show that the weight 12 part of the abelianization of
is 1-dimensional for g ⩾ 8. The computation is done with the aid of computers.
2000 AMS SUBJECT CLASSIFICATION:
Acknowledgment
The authors would like to thank Gwénaël Massuyeau for helpful comments on the first draft of this article.
Funding
The authors were partially supported by KAKENHI (No. 15H03618, No. 15H03619, No. 16H03931, and No. 16K05159), Japan Society for the Promotion of Science, Japan.