Springer Proceedings in Mathematics & Statistics Cheikh Thiécoumbe Gueye Mercedes Siles Molina Editors Non-Associative and Non-Commutative Algebra and Operator Theory NANCAOT, Dakar, Senegal, May 23—25, 2014: Workshop in Honor of Professor Amin Kaidi Springer Proceedings in Mathematics & Statistics Volume 160 Moreinformationaboutthisseriesathttp://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Cheikh Thiécoumbe Gueye • Mercedes Siles Molina Editors Non-Associative and Non-Commutative Algebra and Operator Theory NANCAOT, Dakar, Senegal, May 23–25, 2014: Workshop in Honor of Professor Amin Kaidi 123 Editors CheikhThiécoumbeGueye MercedesSilesMolina DepartementdeMathematiques DepartmentofÁlgebra, etInformatique GeometríayTopología FacultédesSciencesetTechniques, FacultaddeCiencias UniversitéCheikhAntaDiop UniversidaddeMálaga Dakar,Senegal Málaga,Spain ISSN2194-1009 ISSN2194-1017 (electronic) SpringerProceedingsinMathematics&Statistics ISBN978-3-319-32900-0 ISBN978-3-319-32902-4 (eBook) DOI10.1007/978-3-319-32902-4 LibraryofCongressControlNumber:2016949460 ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Dakar’s Workshop in Honor of Professor Amin Kaidi on Non-associative and Non-commutativeAlgebra and Operator Theory took place in May 23–25, 2014, in Dakar, Senegal. The workshop was organized by the LACGAA (Laboratoire d’Algébre, de Cryptologie, de Geométrie Algébrique et Applications) team of Université Cheikh Anta Diop de Dakar in cooperation with the Universities of AlmeríaandMálagainSpain. The workshop received around 30 submissions, and all were reviewed by the programcommittee.Eachpaperwasassignedatleasttotworeviewers.Afterhighly interactivediscussionsand a carefuldeliberation,the programcommitteeselected around20forthisvolume. Theauthorsofacceptedpapersweregiven4weekstopreparethefinalversion fortheseproceedings. We would like to note that Prof. Amin Kaidi is an internationally renowned mathematician. Especially for Senegal, he was the director of the two theses of ProfessorMamadouSangharé.Amanofgreathumanandscientificgenerosity,his support has always been unconditional for us. The scientific cooperation project betweenourlaboratoryandseveraluniversitiesofSpainhasbeenpossiblethanksto him. Wearedeeplygratefultotheprogramcommitteefortheirhardwork,enthusiasm, andconscientiouseffortstoensurethateachreceivedpaperhashadathoroughand fair review. We also would like to thank Ousmane Ndiaye for writing Springer to anacceleratedscheduleforwritingtheproceedings.Wealsowishtoheartilythank Mamadou Sangharé (generalchair), Laila Mesmoudi (organiserchair), as well as theLACGAAteam. Before we end, we would like to thank the Department of Mathematics and InformaticsoftheCheikhAntaDiopUniversityofDakar,theMoroccanEmbassy v vi Preface in Senegal,and the ASTS (Academyof Sciences and Techniquesof Senegal),for theirinvaluablefinancialsupport.Lastbutnotleast,wegivethankstoallthosewho contributedtothisworkshop. Dakar,Senegal CheikhThiécoumbeGueye Málaga,Spain MercedesSilesMolina May2014 Non-Associative and Non-Commutative Algebra and Operator Theory NANCAOT,Dakar, Senegal, May23–25,2014: WorkshopinHonorofProfessorAminKaidi • GeneralChairs: – MamadouSangharé,UniversitéCheikhAntaDiopdeDakar(Senegal) – AntonioCampillo,UniversidaddeValladolid(Spain) • ProgramCo-chairs: – CheikhThiécoumbaGueye,UniversitéCheikhAntaDiopdeDakar(Senegal) – MercedesSilesMolina,UniversidaddeMálaga(Spain) • OrganizationChair: – LailaMesmoudi,UniversitéCheikhAntaDiopdeDakar(Senegal) – IsmailaDiouf,UniversitéCheikhAntaDiopdeDakar(Senegal) ProgramCommittee • AbdellatifRochdi,UniversitéHassanIIMohammedia,Casablanca(Morocco) • AbdelmalekAzizi,UniversitéMohammedPremier,Oujda(Morocco) • AbdenacerMakhlouf,UniversitédeHaute-Alsace(France) • ÁngelRodríguezPalacios,UniversidaddeGranada(Spain) • AntonioPeralta,UniversidaddeGranada(Spain) • ConsueloMartnezLpez,UniversidaddeOviedo(Spain) • DaoudaSangaré,Universitéd’AboboAdjamé,Abidjan(IvoryCoast) • Djibysow,UniversitéCheikhAntaDiopdeDakar(Senegal) • DolorsHerbera,AutonomousUniversityofBarcelona(Spain) • FredvanOystaeyen,UniversityofAntwerp(Belgium) • LaiachiKaoutit,UniversidaddeGranada(Spain) • MauriceMignotte,UniversitédeLouisPasteurdeStrasbourg(France) • MostafaMbekhta,UniversitéLille1(France) • NadiaBoudi,UniversitéMoulayIsmail,Meknès(Morocco) • Nouzhaelyacoubi,UniversitéMohammedV,Agdal,Rabat(Morocco) • OumarDiankha,UniversitéCheikhAntaDiopdeDakar(Senegal) • PatrickSolé,TelecomParisTech,Paris(France) • SaidBenayadi,UniversitédeMetz(France) • MamadouBarry,UniversitéCheikhAntaDiopdeDakar(Senegal) vii viii Non-associativeandNon-commutativeAlgebraandOperatorTheory OrganizationCommittee • AbdoulayeMbaye,UniversitéCheikhAntaDiopdeDakar(Senegal) • AntonioJesúsCalder´nMartín,UniversidaddeCádiz(Spain) • CándidoMartínGonzález,UniversidaddeCádiz(Spain) • CheikhThiécoumbaGueye,UniversitéCheikhAntaDiopdeDakar(Senegal) • DjibySow,UniversitéCheikhAntaDiopdeDakar(Senegal) • DoloresMartínBarquero,UniversidaddeMalagá(Spain) • IsmalaDiouf,UniversitéCheikhAntaDiopdeDakar(Senegal) • LailaMesmoudi,UniversitéCheikhAntaDiopdeDakar(Senegal) • MamadouBarry,UniversitéCheikhAntaDiopdeDakar(Senegal) • MamadouSangharé,UniversitéCheikhAntaDiopdeDakar(Senegal) • MercedesSilesMolina,UniversidaddeMalagá(Spain) • OumarDiankha,UniversitéCheikhAntaDiopdeDakar(Senegal) • SidyD.Tour,UniversitéCheikhAntaDiopdeDakar(Senegal) • MohamedBenMaaouia,UniversitéGastonBergerdeSaint-Louis(Senegal) • AntonioCampillo,UniversidaddeValladolid(Spain) • MaríaVictoriaVelascoCollado,UniversidaddeGranada(Spain) • MaríaIsabelRamírez,UniversidaddeAlmeria(Spain) • JoséMaríaSánchezDelgado,UniversidaddeCadiz(Spain) Contents PartI InvitedTalks 1 GroupTheoryandtheCapitulationProblemforSome NumberFields .............................................................. 3 AbdelmalekAzizi,AbdelkaderZekhnini, andMohammedTaous 2 On Space-Time Codes Arising from Free Modules andAlgebrasoveranIntegralDomain .................................. 27 MhammedBoulagouazandAbdulazizDeajim 3 GradedModulesoverSuperconformalAlgebras....................... 41 ConsueloMartínezandEfimZelmanov 4 OnDeformationsofn-LieAlgebras ...................................... 55 AbdenacerMakhlouf 5 Morita Equivalence and Morita Invariant Properties: Applications in the Context of Leavitt PathAlgebras............................................................... 83 MercedesSilesMolinaandJoséF.SolanillaHernández 6 OnCommutingU-OperatorsinJordanAlgebras...................... 105 IvanShestakov PartII ContributedTalks 7 GradingsonAlgebrasoverAlgebraicallyClosedFields............... 113 AlbertoElduque 8 OntheSetofArtinianSubringsofInfiniteProductsofRings ........ 123 D.KarimandS.Zarzuela ix