$The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$$

The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$

Let $C_n$ be the group of conjugating automorphisms. Valerij G. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases \(n...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org 2023-08
1. Verfasser:	Nasser, Mohamad N
Format:	Artikel
Sprache:	eng
Schlagworte:	Automorphisms Braid theory Representations
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue
container_start_page
container_title	arXiv.org
container_volume
creator	Nasser, Mohamad N
description	Let $C_n$ be the group of conjugating automorphisms. Valerij G. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$ remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards the faithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ is unfaithful in the both cases $n=3$ and $n=4$.
format	Article
fullrecord	<record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2856630779</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2856630779</sourcerecordid><originalsourceid>FETCH-proquest_journals_28566307793</originalsourceid><addsrcrecordid>eNqNjM1KxEAQhAdBcNF9h4a9uIdAnNkkuwdPiyLocY-B0MTOH5ue2D2DPonPa7L6AJ6qq-rrujIr69xDst9Ze2PWqkOapjYvbJa5lfk-dQQN9qFr4plJFXwDyEBfgVh7z4t_w08hril5FRxHEhCahJQ4YLggDGGeacXHaeFrz0Ns545bwBj86GXqeh0VyvtjxeUW-t-PGpWWkB_dHCK_X-5dub0z1w2eldZ_ems2z0-n40syif-IpKEafBSeq8ruszx3aVEc3P-oH4X_Vz4</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2856630779</pqid></control><display><type>article</type><title>The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$</title><source>Freely Accessible Journals</source><creator>Nasser, Mohamad N</creator><creatorcontrib>Nasser, Mohamad N</creatorcontrib><description>Let $C_n$ be the group of conjugating automorphisms. Valerij G. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$ remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards the faithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ is unfaithful in the both cases $n=3$ and $n=4$.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Automorphisms ; Braid theory ; Representations</subject><ispartof>arXiv.org, 2023-08</ispartof><rights>2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Nasser, Mohamad N</creatorcontrib><title>The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$</title><title>arXiv.org</title><description>Let $C_n$ be the group of conjugating automorphisms. Valerij G. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$ remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards the faithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ is unfaithful in the both cases $n=3$ and $n=4$.</description><subject>Automorphisms</subject><subject>Braid theory</subject><subject>Representations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNjM1KxEAQhAdBcNF9h4a9uIdAnNkkuwdPiyLocY-B0MTOH5ue2D2DPonPa7L6AJ6qq-rrujIr69xDst9Ze2PWqkOapjYvbJa5lfk-dQQN9qFr4plJFXwDyEBfgVh7z4t_w08hril5FRxHEhCahJQ4YLggDGGeacXHaeFrz0Ns545bwBj86GXqeh0VyvtjxeUW-t-PGpWWkB_dHCK_X-5dub0z1w2eldZ_ems2z0-n40syif-IpKEafBSeq8ruszx3aVEc3P-oH4X_Vz4</recordid><startdate>20230823</startdate><enddate>20230823</enddate><creator>Nasser, Mohamad N</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20230823</creationdate><title>The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$</title><author>Nasser, Mohamad N</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_28566307793</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Automorphisms</topic><topic>Braid theory</topic><topic>Representations</topic><toplevel>online_resources</toplevel><creatorcontrib>Nasser, Mohamad N</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nasser, Mohamad N</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$</atitle><jtitle>arXiv.org</jtitle><date>2023-08-23</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>Let $C_n$ be the group of conjugating automorphisms. Valerij G. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$ remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards the faithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ is unfaithful in the both cases $n=3$ and $n=4$.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	EISSN: 2331-8422
ispartof	arXiv.org, 2023-08
issn	2331-8422
language	eng
recordid	cdi_proquest_journals_2856630779
source	Freely Accessible Journals
subjects	Automorphisms Braid theory Representations
title	The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms $C_n$ in the cases $n=3$ and $n=4$
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T09%3A51%3A56IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=The%20faithfulness%20of%20an%20extension%20of%20Lawrence-Krammer%20representation%20on%20the%20group%20of%20conjugating%20automorphisms%20%5C(C_n%5C)%20in%20the%20cases%20%5C(n=3%5C)%20and%20%5C(n=4%5C)&rft.jtitle=arXiv.org&rft.au=Nasser,%20Mohamad%20N&rft.date=2023-08-23&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2856630779%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2856630779&rft_id=info:pmid/&rfr_iscdi=true

The faithfulness of an extension of Lawrence-Krammer representation on the group of conjugating automorphisms \(C_n\) in the cases \(n=3\) and \(n=4\)