PROIECT DE CERCETARE
Echivalente de categorii in teoria reprezentarilor de grupuri finite
English version
Informatii
Programul: PN2 IDEI (Informatii privind programul la CNCSIS)
Tipul proiectului: PN-II-ID-PCE-2007-1 (Proiecte de cercetare exploratorie)
Autoritate contractanta: CNCSIS-UEFISCSU
Contractor: Universitatea ,,Babes-Bolyai" Cluj-Napoca
Cod proiect: ID_532
Nr. contract: 29/28.09.2007
Durata de desfasurare: 3 ani, 01.10.2007-30.09.2010
Echipa de cercetare
Prof. univ. dr. Andrei Marcus, director de proiect
Asistent univ. dr. Camelia Dicu, cercetator
Lector univ. dr. Gabriela Olteanu, cercetator
Drd. Constantin Cosmin Todea, asistent cercetare
Drd. Tiberiu Coconet, asistent cercetare
Rezumatul proiectului
Tematica acestui proiect se refera la grupuri finite si reprezentarile lor modulare si proiective, echivalente derivate intre blocuri ale algebrelor grupale, blocuri ale subgrupurilor normale, teorie Clifford, blocuri nilpotente, algebra hiperfocala a unui bloc. Domeniul propus este foarte intens cercetat pe plan international si are multiple ramificatii si aplicatii. Ne propunem o imbinare a metodelor clasice cu metode noi. Ne inscriem in obiectivele generale de abordare ale unor subiecte moderne, de integrare in comunitatea stiintifica internationala si de formare a cercetatorilor tineri. Directii principale de investigare (teoretice si computationale): investigarea din punct de vedere categorial a invariantilor din teoria Clifford legati de conjecturile lui Alperin-Dade-Isaacs-Navarro-Uno, echivalente intre categorii Brauer, invarianta corespondentei Harris-Knoerr la echivalente derivate, algebra hiperfocala a unei extensii de blocuri, obtinerea de echivalente Rickard din isometrii perfecte si izotipii de caractere, reducerea conjecturii Donovan la cazul grupurilor quasisimple, calculul coomologiei de blocuri, calcul de indici Schur.
Activitati
  • Seminar de cercetare: saptamanal, miercuri 10:00-12:00, UBB, cladirea Mathematicum, sala pi.
  • Stagiu de cercetare: Andrei Marcus, 13-20.10.2007, la prof. dr. Stefaan Caenepeel, Vrije Universiteit Brussel (VUB); sustinerea unei conferinte cu titlul Crossed products, Brauer groups and Clifford classes la seminarul de cercetare de algebra al VUB in 19.10.2007.
  • Stagiu de cercetare: Andrei Marcus, 9-16.11.2007, la prof. dr. Thorsten Holm, Otto-von-Guericke-Universität Magdeburg si Leibniz Universität Hannover; sustinerea unei conferinte cu titlul Derived invariance of Clifford classes la seminarul de cercetare de algebra si combinatorica algebrica al Univ. Hanovra in 13.11.2007.
  • Sustinerea publica a tezei de doctorat: Gabriela Olteanu, 19.11.2007, titlul Wedderburn Decomposition of Group Algebras. A Computational Approach with Applications to Schur Groups and Units, Universidad de Murcia, Spania, indrumatori: prof. dr. Ángel del Río si Prof. Dr. Juan Jacobo Simon;
  • Stagiu de cercetare: Gabriela Olteanu, 13.01-17.02.2008, la prof. dr. Ángel del Río, Universidad de Murcia, Spania; introducere in teoria schemelor de asociere (association schemes).
  • Sustinerea publica a tezei de doctorat: Camelia Dicu, 7.03.2008, titlul Metode modul-teoretice in studiul G-algebrelor si al grupurilor punctate, Universitatea Babes-Bolyai Cluj-Napoca, indrumator: prof. dr. Andrei Marcus.
  • Stagiu de cercetare: Tiberiu Coconet, 02.03-08.03.2008, Universität Wuppertal, Germania.
  • Stagiu de cercetare: Andrei Marcus, 27.03-10.04.2008, participare la programul Representation Theory of Finite Groups and Related Topics, ordinary member, Mathematical Sciences Research Institute, Berkeley, USA.
  • Stagiu de cercetare: Tiberiu Coconet, Cosmin Todea, 30.04-04.05.2008, Universität Bielefeld, Germania.
  • Organizare conferinta: International Conference on "Modules and Representation Theory", Universitatea "Babes-Bolyai", Cluj-Napoca, 7-12 Iulie 2008. Sustinerea de catre G. Olteanu a unei conferinte cu titlul Ring isomorfism of cyclic cyclotomic algebras in 08.07.2008.
  • Stagiu de cercetare: Tiberiu Coconet, Andrei Marcus, Gabriela Olteanu, Cosmin Todea, 18-24.08.2008, la Dr. John Murray, National University of Ireland, Maynooth, Irlanda. Sustinerea de catre A. Marcus a unei conferinte cu titlul Derived invariance of Clifford classes, in 19.08.2008 si de catre G. Olteanu a unei conferinte cu titlul Ring isomorphism of cyclic cyclotomic algebras in 22.08.2008.
  • Stagiu de cercetare: Andrei Marcus, 14-27.09.2008, la prof. dr. Changchang Xi, Beijing Normal University, China; sustinerea a trei conferinte la seminarul de cercetare de Teoria Reprezentarilor: Equivalences of categories in modular representation theory, Morita equivalences induced by bimodules over Hopf-Galois extensions, Characters and equivalence classes of central simple group graded algebras.
  • Stagiu de cercetare: Gabriela Olteanu, 4-20.09.2008, la prof. dr. Ángel del Río, Universidad de Murcia, Spania.
  • Stagiu de cercetare: Tiberiu Coconet, Andrei Marcus, 03-10.10.2008, la Dr. Erzsébet Horváth, Budapest Technical University. Sustinerea de catre A. Marcus a unei conferinte cu titlul Hopf-Galois extensions and an exact sequence for H-Picard groups la seminarul de cercetare de algebra al Institutului de Matematica din Budapesta in 06.10.2008.
  • Organizare conferinta: Algebra Symposium, Babes-Bolyai University Cluj-Napoca, May 15-16, 2009. Sustinerea de catre T. Coconet a unei conferinte cu titlul Remarks on induction of G-algebras and skew group algebras in 15.05.2009, si de catre C. Todea a unei conferinte cu titlul New stable elements in Hochschild cohomology algebra in 16.05.2009.
  • Stagiu de cercetare: Gabriela Olteanu, la prof. dr. Ángel del Río, Universidad de Murcia, Spain, Februarie 2009.
  • Stagiu de cercetare: Gabriela Olteanu, Vrije Universiteit Brussel (VUB), Belgia, 1-14 februarie 2009 si 1-30 august 2009, la prof. dr. Eric Jespers; Sustinerea de catre Gabriela Olteanu a conferinte cu titlul A computational approach for the Wedderburn decomposition of group algebras.
  • Stagiu de cercetare: Tiberiu Coconet, Cosmin Todea, 24.08-4.09.2009, la prof. dr. Markus Linckelmann, Universitatea Aberdeen, Marea Britanie.
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    Rezultate
  • Camelia Dicu, On the multiplicity module of a pointed group, Mathematica (Cluj), 50 (73), No.1 (2008), 31-37.
  • Camelia Dicu, Metode modul-teoretice in studiul G-algebrelor si al grupurilor punctate, EFES Publishing House, Cluj-Napoca, 2008, 92pp, ISBN 978-606-526-002-3.
  • Gabriela Olteanu, Wedderburn decomposition of group algebras and applications, EFES Publishing House, Cluj-Napoca, 2008, 165pp, ISBN 978-973-7677-98-3.
  • Gabriela Olteanu, Computation and applications of Schur indices, Proceedings of the International Conference on Modules and Representation Theory (Cluj-Napoca, Romania, July 7-12, 2008), Cluj University Press, Cluj-Napoca, 2009, 149-157.
  • Septimiu Crivei, Gabriela Olteanu, GAP algorithms for finite abelian groups and applications, Carpathian J. Math. 24 (2008), no. 3, 310-316.
  • Allen Herman, Gabriela Olteanu, Ángel del Río, The Schur group of an abelian number field, J. Pure Appl. Algebra 213 (2009), 22-33.
  • Allen Herman, Gabriela Olteanu, Ángel del Río, The gap between the Schur group and the subgroup generated by cyclic cyclotomic algebras, Israel J. Math. 176 (2010), 401-418.
  • Andrei Marcus, Indecomposable modules over group graded skew algebras, Mathematica (Cluj), 50 (73), No.2 (2008), 191-195.
  • Andrei Marcus, Derived invariance of Clifford classes, J. Group Theory, 12 (2009), 83-94.
  • Andrei Marcus, Derived equivalences and  the  abelian defect group conjecture, Proceedings of the  International Conference on Modules and Representation Theory, ''Babes-Bolyai" University Cluj, 2008; Cluj University Press, 111-131.
  • Stefaan Caenepeel, Andrei Marcus, Hopf-Galois extensions and an exact sequence for H-Picard groups, J. Algebra, 323 (2010), 622-657.
  • Simion Breaz, Septimiu Crivei, Andrei Marcus, Proceedings of the International Conference on Modules and Representation Theory, ''Babes-Bolyai" University Cluj, 2008; Cluj University Press, 2009. ISBN 978-973-610-897-6.
  • Constantin Cosmin Todea, Remarks on generalized Brauer pairs, Mathematica (Cluj), 52 (75) (2010), 75-84.
  • Tiberiu Coconet, Remarks on induction of G-algebras and skew group algebras, va aparea in Mathematica (Cluj).
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    Rapoarte
  • Sinteza 2007
  • Sinteza 2008
  • Sinteza 2009
  • Monitorizare 2009 - prezentare
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    Contact

    e-mail:
        marcus at math.ubbcluj.ro
    fax:
        +40 264 591906
    mail:
        Andrei Marcus
        Babes-Bolyai University
        Faculty of Mathematics and Computer Science
        Str. Mihail Kogalniceanu nr. 1
        RO-400084 Cluj-Napoca
        Romania