### Abstract

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

Original language | English |
---|---|

Pages (from-to) | 302-315 |

Number of pages | 14 |

Journal | Experimental Mathematics |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - 3 Jul 2018 |

### Keywords

- Primary 20F28
- Secondary 20J06, 17B40
- free group
- outer automorphism group
- symplectic derivations

## Fingerprint Dive into the research topics of 'An Abelian Quotient of the Symplectic Derivation Lie Algebra of the Free Lie Algebra'. Together they form a unique fingerprint.

## Cite this

Morita, S., Sakasai, T., & Suzuki, M. (2018). An Abelian Quotient of the Symplectic Derivation Lie Algebra of the Free Lie Algebra.

*Experimental Mathematics*,*27*(3), 302-315. https://doi.org/10.1080/10586458.2016.1266975