Periodic polynomial of trace maps

Qing Hui Liu; Jacques Peyrière; Zhi Ying Wen

doi:10.1016/j.bulsci.2006.04.004

Periodic polynomial of trace maps

Qing Hui Liu
, Jacques Peyrière^*
, Zhi Ying Wen

^*Corresponding author for this work

School of Mathematics and Statistics

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

1 Citation (Scopus)

Abstract

Let σ be an endomorphism of the free group on two generators and Φ_σ the trace map associated with σ. A polynomial P is said to be periodic for σ if, for some positive integer n, it is invariant under Φ_σⁿ, i.e., P ○ Φ_σⁿ = P. In this note we study the structure of the ring of periodic polynomials for σ.

Original language	English
Pages (from-to)	572-582
Number of pages	11
Journal	Bulletin des Sciences Mathematiques
Volume	131
Issue number	6
DOIs	https://doi.org/10.1016/j.bulsci.2006.04.004
Publication status	Published - Sept 2007

Keywords

Free groups
Fricke characters
Trace maps

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10.1016/j.bulsci.2006.04.004

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@article{51523efe2d9e412d88290cefdabb9150,

title = "Periodic polynomial of trace maps",

abstract = "Let σ be an endomorphism of the free group on two generators and Φσ the trace map associated with σ. A polynomial P is said to be periodic for σ if, for some positive integer n, it is invariant under Φσn, i.e., P ○ Φσn = P. In this note we study the structure of the ring of periodic polynomials for σ.",

keywords = "Free groups, Fricke characters, Trace maps",

author = "Liu, \{Qing Hui\} and Jacques Peyri{\`e}re and Wen, \{Zhi Ying\}",

year = "2007",

month = sep,

doi = "10.1016/j.bulsci.2006.04.004",

language = "English",

volume = "131",

pages = "572--582",

journal = "Bulletin des Sciences Mathematiques",

issn = "0007-4497",

publisher = "Elsevier Masson s.r.l.",

number = "6",

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TY - JOUR

T1 - Periodic polynomial of trace maps

AU - Liu, Qing Hui

AU - Peyrière, Jacques

AU - Wen, Zhi Ying

PY - 2007/9

Y1 - 2007/9

N2 - Let σ be an endomorphism of the free group on two generators and Φσ the trace map associated with σ. A polynomial P is said to be periodic for σ if, for some positive integer n, it is invariant under Φσn, i.e., P ○ Φσn = P. In this note we study the structure of the ring of periodic polynomials for σ.

AB - Let σ be an endomorphism of the free group on two generators and Φσ the trace map associated with σ. A polynomial P is said to be periodic for σ if, for some positive integer n, it is invariant under Φσn, i.e., P ○ Φσn = P. In this note we study the structure of the ring of periodic polynomials for σ.

KW - Free groups

KW - Fricke characters

KW - Trace maps

UR - https://www.scopus.com/pages/publications/34547854314

U2 - 10.1016/j.bulsci.2006.04.004

DO - 10.1016/j.bulsci.2006.04.004

M3 - Article

AN - SCOPUS:34547854314

SN - 0007-4497

VL - 131

SP - 572

EP - 582

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 6

ER -

Periodic polynomial of trace maps

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Keywords

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