Invariant bases for free lie rings

R. M. Bryant; L. G. Kovács; Ralph Stöhr

doi:10.1093/qjmath/53.1.1

Invariant bases for free lie rings

R. M. Bryant^*, L. G. Kovács, Ralph Stöhr

^*Corresponding author for this work

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

11 Citations (Scopus)

Abstract

Let L denote the free Lie ring of rank 2r with free generators x _i, y_i (1 ≤ i ≤ r), and let τ be the automorphism of L that interchanges x_i and y_i for all i. We construct a ℤ-basis of L that consists of pairs of elements which are interchanged by τ, and elements upon which τ acts as multiplication by -1.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Quarterly Journal of Mathematics
Volume	53
Issue number	1
DOIs	https://doi.org/10.1093/qjmath/53.1.1
Publication status	Published - Mar 2002

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10.1093/qjmath/53.1.1

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title = "Invariant bases for free lie rings",

abstract = "Let L denote the free Lie ring of rank 2r with free generators x i, yi (1 ≤ i ≤ r), and let τ be the automorphism of L that interchanges xi and yi for all i. We construct a ℤ-basis of L that consists of pairs of elements which are interchanged by τ, and elements upon which τ acts as multiplication by -1.",

author = "Bryant, {R. M.} and Kov{\'a}cs, {L. G.} and Ralph St{\"o}hr",

year = "2002",

month = mar,

doi = "10.1093/qjmath/53.1.1",

language = "English",

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T1 - Invariant bases for free lie rings

AU - Bryant, R. M.

AU - Kovács, L. G.

AU - Stöhr, Ralph

PY - 2002/3

Y1 - 2002/3

N2 - Let L denote the free Lie ring of rank 2r with free generators x i, yi (1 ≤ i ≤ r), and let τ be the automorphism of L that interchanges xi and yi for all i. We construct a ℤ-basis of L that consists of pairs of elements which are interchanged by τ, and elements upon which τ acts as multiplication by -1.

AB - Let L denote the free Lie ring of rank 2r with free generators x i, yi (1 ≤ i ≤ r), and let τ be the automorphism of L that interchanges xi and yi for all i. We construct a ℤ-basis of L that consists of pairs of elements which are interchanged by τ, and elements upon which τ acts as multiplication by -1.

UR - http://www.scopus.com/inward/record.url?scp=0344585298&partnerID=8YFLogxK

U2 - 10.1093/qjmath/53.1.1

DO - 10.1093/qjmath/53.1.1

M3 - Article

SN - 0033-5606

VL - 53

SP - 1

EP - 17

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 1

ER -

Invariant bases for free lie rings

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