English Version

Grupuri, grupuri cuantice, coringuri si teoria reprezentarii

Groups, quantum groups, corings and representation theory



Contract nr. 24/28.09.2007 din cadrul PN-II, programul "Idei"


Director: Prof.Dr. Gigel Militaru



Articole publicate—Published papers

  1. B. Ion, Standard bases for affine parabolic modules and nonsymmetric Macdonald polynomials, J. Algebra, 319 (2008), 3480-3517.
  2. M.C. Iovanov, J. Vercruysse, Cofrobenius corings and adjoint functors, Journal of Pure and Applied Algebra, Vol. 212 (2008), Issue 9, 2011-2146.
  3. M.C. Iovanov, Frobenius Extensions of Corings, Commun. Algebra 36 (2008), no. 3, 869-892.
  4. M.C. Iovanov, C. Nastasescu, B. Torrecillas-Jover, The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras, J. Algebra 320 (2008), 2144-2155.
  5. A.L. Agore, G. Militaru, Crossed Product of groups. Applications. Arabian J. Sci. and Engineering (AJSE), 33 (2008), 1-17
  6. A. L. Agore, A. Chirvasitu, B. Ion, G. Militaru: Bicrossed products for finite groups, Algebras and Representation Theory, 12(2009), 481-488
  7. M. Beattie, M.C. Iovanov, S. Raianu, The Antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective, Algebras and Representation Theory 12 (2009), 251-255.
  8. M.C. Iovanov, The Generating Condition for Coalgebras, Bulletin of the London Mathematical Society 41 (2009), no.3, 483-494.
  9. M.C. Iovanov, When does the Rational Torsion Split off for Finitely Generated Modules, Algebras and Representation theory (2009), no. 2-5, 287-309.
  10. B. Ion, Generalized exponents of small representations. I, Representation Theory, 13 (2009) 401-426.
  11. G. Militaru, Serre Theorem for involutory Hopf algebras, Centr. Eur. J. Math, Vol. 8, Issue 1 (2010), 15-21.
  12. A. L. Agore, D. Fratila, Crossed products of cyclic groups, acceptat pentru publicare in Czechoslovak Mathematical Journal.
  13. A. L. Agore, Categorical constructions for Hopf algebras, acceptat spre publicare in Commun. Algebra.
  14. A.L. Agore, Monomorphisms of coalgebras, acceptat spre publicare in Colloq. Math.
  15. M.C. Iovanov, L. Kadison, "When is a weak quasi-Hopf algebra Frobenius", acceptat spre publicare in Proc. AMS.
  16. A. L. Agore, G. Militaru, Deformation of a matched pair and Schreirer type theorems for bicrossed product of groups, trimis spre publicare
  17. A.L. Agore, Limits of coalgebras, bialgebras and Hopf algebras, acceptat spre publicare in Proc. Amer. Math Soc.
  18. B. Ion, A Poincare-Birkhoff-Witt theorem for Hopf algebras with central coradical, trimis spre publicare
  19. B. Ion, Generalized exponents of small representations. II., va apre in Representation Theory.
  20. M.C. Iovanov, Abstract Integrals in Algebra, trimis spre publicare.
 Echipa proiectului—The team of the project:
    - Ana Loredana Agore (ana.agore fmi.unibuc.ro)
    - Bogdan Ion,
    - Dragos Fratila (dragos.fratila fmi.unibuc.ro)
    - Gigel Militaru,
    - Miodrag Cristian Iovanov (pagina personala)

 Rezumatul proiectului—Abstract of the project

 Gradul de implicare al tinerilor cercetatori—The young people of the project

 Obiectivele programului - Project Objectives

 Bugetul

 Obiective si activitati si gradul de realizare. Rezultate obtinute—Objectives, Activities. Results

 Actiuni desfasurate in cadrul programului

 Rapoarte
        2007
            - Raport de sinteza detaliat
            - Raport de autoevaluare

        2008
            - Raport de sinteza detaliat
            - Raport de autoevaluare

        2009 etapa intermediara
            - Raport de sinteza detaliat
            - Deviz post calcul

        2009 etapa finala
            - Raport de sinteza detaliat
            - Raport de autoevaluare


 Expunerea la sedinta publica de monitorizare CNCSIS 30.10.09: performanta si cheltuieli din grant



Algebre Hopf si teme inrudite
Hopf algebras and related topics

  

Grant no. 88/05.10.2011 of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI - PN II Idei

The Team:

  • Prof. Dr. Gigel Militaru (the team leader of the project),
  • CS III Sebastian Burciu,
  • CS III Bogdan Ion,
  • AC Ana-Loredana Agore (PhD student - PhD since 1/10/2012),
  • AC Costel Gabriel Bontea (PhD student).

Project Summary:

Hopf algebras were introduced around 1960 arising from algebraic geometry and algebraic topology. The second important development within this field of study started in 1987 with the appearance of the paper Quantum groups by V. Drinfel"d. The project will be focused on both parts (classic and quantum) of the theory of Hopf algebras and has two corresponding general objective each of them with several open problems. Objective I: New structural results for Hopf algebras. There are four open problems related to this objective. Objective II: Categorical methods in quantum groups. Braided, monoidal and fusion categories. There are five open problems related to the second objective.

Annual scientific reports (in romanian): 2011, 2012

Actual annual expenses: 2011, 2012

Published/Accepted papers in ISI journals (the impact factor for 2011 is given):

  1. S. Burciu, S. Natale - Fusion rules of equivariantizations of fusion categories, Journal of Mathematical Physics, 54(2013), 013511; DOI: 10.1063/1.4774293 (IF: 1.291). Link
  2. A. L. Agore, G. Militaru - Classifying complements for Hopf algebras and Lie algebras, Journal of Algebra, 391(2013), 193-208 (IF: 0,613) Link
  3. A. L Agore – Coquasitriangular structures for extensions of Hopf algebras, Glasgow Math. J. 55 (2013), 1-15. (IF: 0.571)
  4. A. L. Agore, C. G. Bontea, and G. Militaru – Classifying coalgebra split extensions of Hopf algebras, J. Algebra Appl. 12 (2013), 1-24. (IF: 0.483)
  5. A. L. Agore, G. Militaru – Unified products and split extensions of Hopf algebras, Contemporary Math. AMS, Vol. 585 (2013), 1-15.
  6. A. L. Agore, S. Caenepeel, G. Militaru – The center of the category of bimodules and descent data for non-commutative rings, J. Algebra Appl. 11 (2012), 1-17. (IF: 0.483)
  7. G. Militaru – Representable functors for corings, Comm. Algebra 40 (2012), no.5, 1766-1796. (IF: 0.347)
  8. A. L. Agore and G. Militaru – Schreier type theorems for bicrossed products, Cent. Eur. J. Math. 10 (2012), no.2, 722-739. (IF: 0.440)
  9. A. L. Agore, G. Militaru – Extending structures for Lie algebras, accepted for publications in Monatshefte für Mathematik (IF: 0,616)
  10. A. L. Agore, G. Militaru – Classifying complements for Hopf algebras and Lie algebras, accepted for publication in Journal of Algebra, DOI: 10.1016/j.jalgebra.2013.06.012 (IF: 0,613)
  11. A.L. Agore, S. Caenepeel, G. Militaru – Braidings on the category of bimodules, Azumaya algebras and epimorphisms of rings, in press Applied Cat. Structures – DOI: 10.1007/s10485-012-9294-3. (IF: 0.600)
  12. A.L. Agore, G. Militaru – Extending structures I: the level of groups, in press, Algebr. Represent. Theory, DOI: 10.1007/s10468-013-9420-4. (IF: 0.595)
  13. A. L. Agore, C. G. Bontea, G. Militaru – Classifying bicrossed products of Hopf algebras, in press Algebr. Represent. Theory, DOI:10.1007/s10468-012-9396-5. ( IF: 0.595).
  14. S. Burciu – Kernels of representations of Drinfel’d doubles of finite groups, accepted for publications in Cent. Eur. J. Math. (IF: 0.440)
  15. S. Burciu – Subgroups of odd depth – a necessary condition, accepted for publications in Czechoslovak J. Math. (IF: 0.262)
  16. C. G. Bontea – Classifying bicrossed products of two Sweedler.s Hopf algebras, accepted for publications in Czechoslovak J. Math. (IF: 0.262)

Papers submitted for publication:

  1. S. Burciu – On coideal subalgebras of cocentral Kac algebras and a generalization of Wall’s conjecture, submitted.
  2. S. Burciu – On the irreducible representations of generalized quantum doubles, submitted
  3. A. L. Agore, G. Militaru – Classifying complements for groups. Applications, submitted
  4. A. L. Agore, C. G. Bontea, and G. Militaru – The classification of all crossed products H4 # k[Cn], submitted
  5. A. L. Agore, G. Militaru – The extending structures problem for algebras, submitted.
  6. V. Chari, B. Ion – BGG reciprocity for current algebras, submitted.

Dissemination of the scientific results. Talks given at international conferences:

  1. G. Militaru - Classifying bicrossed products of quantum groups, Algebra Geometry Mathematical Physics, Brno, september 2012.
  2. G. Militaru - Extending structures: the level of groups, Groups and their actions, Bedlewo, July 2012.
  3. A.L. Agore - Bicrossed descent theory of exact factorizations and the number of types of groups of finite order , Groups and their actions, Bedlewo, July 2012
  4. C. Bontea - Classifying crossed product of quantum groups, Algebra Geometry Mathematical Physics(AGMP), Brno, September 2012.
  5. A. L. Agore - Deformations and descent type theory for Hopf algebras, Algebra Geometry Mathematical Physics, Brno, September 2012.
  6. G. Militaru - Classifying bicrossed products. Deformations and descent type theory for quantum groups, Hopf Algebra Workshop, Brussel VUB, 19 March 19, 2012.
  7. A.L. Agore - Classifying exact factorizations of a group through a given subgroup and the number of types of groups of finite order, 2nd Biennial Groups Theory Conference, Dogus University, Istanbul, February 2013.
  8. A.L. Agore - The factorization problem for Lie algebras, International workshop Lie theory and its applications, Varna, Bulgaria, June 2013.
  9. A.L. Agore - Exact factorizations for Hopf algebras. Applications, Joint international meeting of AMS and RMS , Alba-Iulia, Romania, June 2013.
  10. A.L. Agore - Bicrossed products of Hopf algebras, Workshop for young researchers, Constanta, Romania, May 2013.
  11. A.L. Agore - Classifying complements for Hopf algebras, Lie algebras and groups, Workshop "Rings, categories and Hopf algebras", Bucharest, May 2013.
  12. C.G. Bontea - The factorization problem for Hopf algebras, Workshop "Rings, categories and Hopf algebras", Bucharest, May 2013.
  13. G. Militaru - The Extending Structures Problem, 2nd Biennial Groups Theory Conference, Dogus University, Istanbul, February, 2013
  14. G. Militaru - The extending structures for algebras, Workshop "Rings, categories and Hopf algebras", Bucharest, May 2013.
  15. G. Militaru - Extending structures for Lie algebras, International workshop Lie theory and its applications, Varna, Bulgaria, June 2013.
  16. G. Militaru - The extension problem for Hopf algebras, Joint international meeting of AMS and RMS, Alba-Iulia, Romania, June 2013.
  17. S. Burciu - Kernels of representations and coideal subalgebras of Hopf algebras Workshop "Rings, Categories and Hopf Algebras", May 18-19, 2013, Bucharest.

2002 - 2015 -- Facultatea de Matematica si Informatica, Universitatea din Bucuresti
Str. Academiei nr. 14, sector 1, C.P. 010014, Bucuresti, Romania
Tel: (4-021) 314 2863, Fax: (4-021) 315 6990, secretariat fmi.unibuc.ro