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

Shigeyuki Morita; Takuya Sakasai; Masaaki Suzuki

doi:10.1080/10586458.2016.1266975

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

Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki

Department of Frontier Media Science

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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	https://doi.org/10.1080/10586458.2016.1266975
Publication status	Published - 3 Jul 2018

Keywords

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

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10.1080/10586458.2016.1266975

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title = "An Abelian Quotient of the Symplectic Derivation Lie Algebra of the Free Lie Algebra",

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.",

keywords = "Primary 20F28, Secondary 20J06, 17B40, free group, outer automorphism group, symplectic derivations",

author = "Shigeyuki Morita and Takuya Sakasai and Masaaki Suzuki",

note = "Funding Information: The authors were partially supported by KAKENHI (No. 15H03618, No. 15H03619, No. 16H03931, and No. 16K05159), Japan Society for the Promotion of Science, Japan. Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Taylor & Francis.",

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AU - Sakasai, Takuya

AU - Suzuki, Masaaki

N1 - Funding Information: The authors were partially supported by KAKENHI (No. 15H03618, No. 15H03619, No. 16H03931, and No. 16K05159), Japan Society for the Promotion of Science, Japan. Publisher Copyright: © 2018, © 2018 Taylor & Francis.

PY - 2018/7/3

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N2 - 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.

AB - 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.

KW - Primary 20F28

KW - Secondary 20J06, 17B40

KW - free group

KW - outer automorphism group

KW - symplectic derivations

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JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

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ER -

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

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Keywords

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