An Abelian Quotient of the Symplectic Derivation Lie Algebra of the Free Lie Algebra

Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki

Research output: Contribution to journalArticle

Abstract

We construct an abelian quotient of the symplectic derivation Lie algebra hg,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 hg,1 is 1-dimensional for g ⩾ 8. The computation is done with the aid of computers.

Original languageEnglish
Pages (from-to)302-315
Number of pages14
JournalExperimental Mathematics
Volume27
Issue number3
DOIs
Publication statusPublished - 3 Jul 2018

Keywords

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

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