English Version

CONTRACT IDEI 1005 nr. 434/1.10.2007

Descriere succinta a proiectului de cercetare

Proiectul abordeaza mai multe directii actuale de cercetare din algebra necomutativa: algebre Hopf si algebre quasi-Hopf, coinele, categorii braided monoidale, module ingemanate, functori involutivi, arbori binari. Obiectivele proiectului sunt:
1. Obtinerea unor rezultate de clasificare pentru algebre Hopf si algebre quasi-Hopf finit dimensionale.
2. Studiul functorilor tare involutivi pe categorii abstracte si obtinerea unor teoreme generale de tip Moore-Penrose.
3. O teorie a coinelelor in categorii braided monoidale ce admit conuclee, cu aplicatii in teoria structurilor ingemanate.
4. Realizarea unui studiu sistematic al modulelor ingemanate in categorii braided monoidale si descrierea acestora ca si categorii de comodule peste un coinel sau ca si categorii de module peste o algebra monoidala.
5. Unificarea rezultatelor obtinute in ceea ce priveste categoriile de module Hopf peste diverse algebre Hopf sau generalizari ale acestora folosind limbajul si tehnicile categoriilor braided monoidale.
6. Folosind limbajul categoriilor braided monoidale, sa gasim conditii necesare si suficiente pentru care structura de algebra data de un produs smash indus de un braiding local si cea de coalgebra data de un coprodus smash (indusa de asemenea de un braiding local) sa ofere unui anumit obiect o structura de bialgebra si, respective, de algebra Hopf in categorie.
7. O K-teorie pentru coalgebre si algebre Hopf.
8. Abordarea unor probleme de combinatorica privind arborii binari cu ajutorul unor structuri algebrice cuantice.

Echipa de cercetare este alcatuita din trei cercetatori cu experienta si doi doctoranzi.
Tematica celor doua teze de doctorat se incadreaza in obiectivele acestui proiect.

Director de proiect

Prof.dr. Constantin Nastasescu, Facultatea de Matematica si Informatica a Universitatii din Bucuresti.

Seminarii de lucru

 Data  Titlul seminarului
 9.10.2007  Clasificarea algebrelor Hopf finit dimensionale
 12.11.2007  Studiul functorilor involutivi
 10.12.2007  Conceptului de coinel intr-o categorie monoidala
 20.02.2008  Studiul modulelor ingemanate cu ajutorul C-categoriilor
 21.04.2008  Clasificarea algebrelor Hopf punctuate
 22.05.2008  Deformari ale algebrelor graduate
 25.09.2008  Unificarea categoriilor de module Hopf definite peste diferite tipuri de algebra Hopf generalizate
 12.11.2008  Studiul unor ecuatii neliniare
 19.12.2008  Studiul coactiunilor pe spatii de morfisme
 04.02.2009  Studiul algebrelor Hopf co-Frobenius
 30.03.2009  Algebre Hopf incrucisate in categorii braided
 19.06.2009  Coactiuni de algebre Hopf
 24.09.2009  Algebre Hopf de dimensiune finita

Echipa de cercetare a grantului:



Cercetare sprijinita financiar de acest grant:

1. G. Barad, On a remark of Loday about the associahedron and algebraic K-theory, An.St. Univ. Ovidius Constanta vol.16 (1), 5-18, 2008.
2. M. C. Iovanov, C. Nastasescu, J. B. Torrecillas, The Dickson subcategory splitting conjecture for pseudocompact algebras, J. Algebra 320 , 2144-2155, 2008.
3. G. Barad, Finding Eulerian cycle decompositions and the rotation distance between binary trees, Bull. Math. Soc. Sci. Math. Roumanie, Tome 51(99), no 1, 21-38, 2008.
4. S. Dascalescu, Group gradings on diagonal algebras, Arch. Math. 91, No. 3, 212-217 (2008).
5. M. Beattie, D. Bulacu, Braided Hopf algebras obtained from coquasitriangular Hopf algebras, Commun. Math. Phys. 282, 115-160, 2008.
6. F. I. Castano, N. Chifan, C. Nastasescu, Localization on certain Grothendieck categories, Acta Mathematica Sinica, English Series Vol. 25, No. 3, 379-392, 2009.
7. S. Dascalescu, C. Nastasescu, M. Nastasescu, Strongly involutory functors, Commun. Algebra 37, No. 5, 1677-1689, 2009.
8. L. Daus, C. Nastasescu, F. Van Oystaeyen, V-Categories: Applications to Graded Rings, Commun. Algebra 37, No. 9, 3248 - 3258, 2009.
9. M. Beattie, D. Bulacu, On the Antipode of a Co-Frobenius (Co)Quasitriangular Hopf Algebra, Commun. Algebra 37, No. 9, 2981 - 2993, 2009.
10. D. Bulacu, S. Caenepeel, J. B. Torrecillas, Involutory quasi-Hopf algebras, Algebr. Represent. Theory 12, No. 2-5, 257-285, 2009.
11. G. Barad, A nonlinear equation which unify the quantum Yang-Baxter equation and the Pentagonal equation. A Hopf algebra approach, acceptata spre publicare in Bull. Math. Soc. Sci. Math. Roumanie, 2009.

In iunie 2008 G. Barad a obtinut titlul de doctor in matematica la U.B. cu teza "Transformari locale de structuri : flipuri triangulare, rotatii de arbori binari si obstructii combinatoriale de sortare", coordonator Prof. C. Nastasescu.




Raportari

Prof.dr. Dascalescu Sorin

  


Data si locul nasterii: Nascut la 23 Aprilie 1964 in Ploiesti.

Educatia: A absolvit Facultatea de Matematica, Universitatea Bucuresti in 1988.
Functiile didactice: profesor la Liceul Colorom Codlea intre 1988-1990, asistent intre 1990-1995, lector intre 1995-1999, conferentiar intre 1999-2001 iar din 2001 este Profesor la Facultatea de Matematica si Informatica, Universitatea Bucuresti.
Teza de doctorat: A sustinut doctoratul in 1992 cu teza ''Inele Graduate de Suport Finit''.
Cursuri predate: A tinut cursuri Algebre Hopf, Inele graduate si teorie Clifford, Algebra (I si II), Reprezentari de algebre, Algebre si coalgebre.
Domenii de cercetare: Algebre Hopf, Teoria Inelelor, Grupuri Cuantice.

Este recenzent la Zentralblatt fur Mathematik si Mathematical Reviews.
A obtinut Premiul "Gheorghe Lazar" al Academiei Romane, pentru anul 1996.

Carti si manuale

  1. Hopf algebras: an introduction, Monographs in Pure and Applied Mathematics 235(2000), Marcel Dekker, New York, 401 pag (cu C.Nastasescu si S.Raianu)
  2. Algebre Hopf, Editura Universitatii Bucuresti, 1998, 140 pag. (cu C.Nastasescu si S.Raianu).
  3. Probleme de algebra, Editura Universitatii Bucuresti, 1993, 100 pag., (cu C.Baetica).

Articole stiintifice

  1. Graded T-rings, Comm. Algebra, 17, 1989, p.3033-3042 (cu C.Nastasescu).
  2. The equation xn=a in left cancellative monoids, Rivista di Matematica Pura ed. Appl., Udine, 9, 1991, p.95-115 (cu C.Nastasescu).
  3. Some results on graded rings of finite support, Proc. of the Algebra Conf., Babes-Bolyai University, Faculty of Mathematics and Computer Science Research Seminars no.1, 1992, p.131-136.
  4. A note on groups with the finite embedding property, Proc. of the Int. Conf. on Group Theory, Timisoara, 1992, p.43-45.
  5. Graded semiperfect rings, Bull. de la Soc. Sci. Math. Roumaine, 36, 1992, p.247-255.
  6. Graded T-rings with finite support, Comm. Algebra, 21, 1993, p.3619-3636, (cu A. del Rio).
  7. A Maschke-type theorem for crossed coproducts, Annals of the Ovidius University of Constanta, 2, 1994, p.44-51 (cu S.Caenepeel si S.Raianu).
  8. A note on intermediate normalizing extensions, Bull.of the Austral. Math. Soc., 50, 1994, p.313-316 (cu L. Van Wyk).
  9. A note on graded semilocal rings, Revue Roumaine de Math. Pures et Appl., 40, 1995, p.253-258 (cu M.Beattie si C.Nastasescu).
  10. Graded coalgebras and Morita-Takeuchi contexts, Tsukuba J. Math., 19, 1995, p.395-407 (cu C.Nastasescu, S.Raianu si F. Van Oystaeyen).
  11. Finite Hopf-Galois coextensions, crossed coproducts and duality, J. Algebra 178, 1995, p.400-413 (cu S.Raianu si Y.H. Zhang).
  12. Cosemisimple Hopf algebras coacting on coalgebras, Comm. Algebra, 24, 1996, p.1649-1678 (cu S.Caenepeel si S.Raianu).
  13. Gradings of finite support. Applications to injective objects, J. Pure Appl. Algebra, 107, 1996, p.193-206 (cu C.Nastasescu, A. del Rio si F. Van Oystaeyen).
  14. Categories of modules graded by G-sets. Applications, J. Pure Appl. Algebra 107, 1996, p.129-139 (cu M.Beattie).
  15. Do isomorphic structural matrix rings have isomorphic graphs?, Proc. Amer. Math. Soc., 124, 1996, p.1385-1391 (cu L. Van Wyk).
  16. Crossed coproducts and cleft coextensions, Comm. Algebra 24, 1996, p.1229-1243 (cu G.Militaru si S.Raianu).
  17. Coalgebra deformations of bialgebras by Harrison cocycles, Bull. Belgian Math. Soc. 4(1997), 647-672 (cu S.Caenepeel, G.Militaru si F.Panaite).
  18. Some Remarks on a theorem of H.-J. Schneider, Comm. Algebra 24 (1996), p.4477-4493 (cu S.Raianu si F. Van Oystaeyen).
  19. Comodules graded by G-sets. Applications, Comm. Algebra 25 (1997), p.159-175 (cu C.Nastasescu, B.Torrecillas si F. Van Oystaeyen).
  20. Duality theorems for graded algebras and coalgebras, J. Algebra 192 (1997), p.261-276, (cu C.Nastasescu, B.Torrecillas si F. Van Oystaeyen).
  21. Galois Extensions for Co-Frobenius Hopf Algebras, J. Algebra 198 (1997), p.164-183, (cu M.Beattie si S.Raianu).
  22. Modules Graded By G-Sets. Duality And Finiteness Conditions, J. Algebra 195 (1997), p.624-633, (cu D.Bulacu si L.Grünenfelder).
  23. Comodules graded by G-sets. Applications, Comm. Algebra 25 (1997), p.159-175, (cu C.Nastasescu, B.Torrecillas si F. Van Oystaeyen).
  24. FBN Hopf Module Algebras, Comm. Algebra 25 (1997), p.3521-3529, (cu A.V. Kelarev si B.Torrecillas).
  25. Pointed Hopf algebras of dimension p3, J. Algebra 209 (1998), p.622-634, (cu S.Caenepeel).
  26. Finiteness Conditions, Co-Frobenius Hopf Algebras and Quantum Groups, J. Algebra 200 (1998), p.312-333, (cu M.Beattie, L.Grünenfelder si C.Nastasescu).
  27. On pointed Hopf algebras of dimension 2n, Bull. London Math. Soc. 31 (1999), p.17-24, (cu S.Caenepeel).
  28. On the number of types of finite dimensional Hopf algebras, Inventiones Math. 136 (1999), p.1-7, (cu M.Beattie si L.Grünenfelder).
  29. Classifying pointed Hopf algebras of dimension 16, Comm. Algebra 28 (2000), p.541-568 (cu S.Caenepeel si S.Raianu).
  30. On pointed Hopf algebras of dimension pn, Proc. Amer. Math. Soc. 128 (2000), p.361-367, (cu M.Beattie si L.Grünenfelder).
  31. Yang-Baxter operators arising from (co)algebra structures, Comm. Algebra 27 (1999), p.5833-5845, (cu F.Nichita).
  32. Group gradings on full matrix rings, J. Algebra 220 (1999), p.709-728 (cu B.Ion, C.Nastasescu si J.Rios).
  33. Pointed Hopf algebras with large coradical, Comm. Algebra 27 (1999), p.4821-4826, (cu S.Dascalescu).
  34. Forms of Hopf algebras, Manuscripta Math. 100 (1999), p.35-53, (cu S.Caenepeel si L. Le Bruyn).
  35. A co-Frobenius Hopf algebra with a separable Galois extension is finite, Proc. Amer. Math. Soc. 128(2000), 3201-3203 (cu M.Beattie si S.Raianu).
  36. Constructing pointed Hopf algebras by Ore extensions, J. Algebra 225 (2000), p.743-770, (cu M.Beattie si L.Grünenfelder).
  37. Co-Frobenius Hopf algebras: integrals, Doi-Koppinen modules and injective objects, J. Algebra 220 (1999), p.542-560, (cu C.Nastasescu si B.Torrecillas).
  38. The categories of Yetter-Drinfel'd modules, Doi-Hopf modules and two-sided two-cosided Hopf modules, Applied Categorical Structures 6 (1998), p.223-237, (cu M.Beattie, S.Raianu si F. Van Oystaeyen).
  39. Smash (Co)-products from adjunctions, "Rings, Hopf algebras and Brauer Groups", Marcel Dekker Lecture Notes, 197 (1998), p.103-110, (cu S.Raianu si F. Van Oystaeyen).
  40. Strongly graded coalgebras and graded crossed coproducts, ''Abelian groups, module theory, and topology'', editors D. Dikranjan si L. Salce, Proceedings of the conference in honour of A. Orsatti, Padua, Italy, Marcel Dekker Lecture Notes 201 (1998), p.131-142, (cu C.Nastasescu si S.Raianu).
  41. Finiteness conditions for semigroup graded modules, Rev. Roumaine Math. Pures. Appl 44 (1999), p.37-50 (cu A.V.Kelarev).
  42. On gradings of matrix algebras by cyclic groups, Comm. Algebra 29 (2001), 5013-5021 (cu C.Boboc).
  43. Homological dimension of coalgebras and crossed coproducts, K-Theory 23 (2001), 53-65 (cu C.Nastasescu si B.Torrecillas).
  44. The recovery of the non-diagonal tile in a tiled triangular matrix ring, Indian J. Math. 42 (2000), 167-173 (cu L.Van Wyk).
  45. Semigroup gradings of upper triangular matrix rings, Rev. Roumaine Math. Pures Appl. 46(2001), 611-615 (cu A.Kelarev si C.Nastasescu).
  46. Semigroup gradings of full matrix rings, Comm. Algebra 29 (2001), 5023-5031 (cu A.Kelarev si L.Van Wyk).
  47. Involutory Hopf algebras with non-zero integral, Bull. London Math. Soc. 34 (2002), 33-36 (cu C.Nastasescu si B.Torrecillas).
  48. On gradings of matrix algebras and descent theory, Comm. Algebra 30 (2002), 5901-5920 (cu S.Caenepeel si C.Nastasescu).
  49. Lifting of Nichols algebras of type B2, Israel J. Math. 132 (2002), 1-28 (cu M.Beattie si S.Raianu).
  50. Co-Frobenius Hopf algebras and the coradical filtration, Mathematische Zeitschrift 243 (2003), 145-154 (cu N.Andruskiewitsch).
  51. Group gradings on M2(k), Bull. Australian Math. Soc. 68 (2003), 285-293 (cu R.Khazal si C.Boboc).
  52. Isomorphism of generalized triangular matrix rings and recovery of tiles, International Journal of Mathematics and Math. Sciences 9 (2003), 533-538 (cu R.Khazal si L.Van Wyk).
  53. Hopf algebras of dimension 14, Journal of the London Math. Soc. 69 (2004), 65-78 (cu M.Beattie).
  54. Quantum lines over non-cocommutative Hopf algebras, J. Algebra 273 (2004), 753-779 (cu C.Calinescu, A.Masuoka si C.Menini).
  55. Some examples of integrals for bialgebras, Hopf algebras, 133-141, Lecture Notes in Pure Appl. Math. 237 (2004), Marcel Dekker.
  56. On associative superalgebras of matrices, Rocky Mountain J. Math. 34 (2004), 585-598 (cu P.Jarvis, A.Kelarev si C.Nastasescu).
  57. Symmetric liftings of quantum linear spaces, Mathematica 46 (69) (2004), 141-147.
  58. Periodic rings with finitely generated underlying group, International Journal of Mathematics and Math. Sciences 36 (2004), 1887-1892 (cu R.Khazal).
  59. Symmetric coalgebras, Journal of Algebra 279 (2004), 326-344 (cu F.Castano Iglesias si C.Nastasescu).
  60. Wide Morita contexts, relative injectivity and equivalence results, Journal of Algebra 284 (2005), 705-736 (cu C.Chifan si C.Nastasescu).
  61. On quantum groups at -1, Algebras and Representation Theory 8 (2005), 11-34 (cu N.Andruskiewitsch).
  62. Good gradings on matrix algebras by finite abelian groups of prime index, Bull. Math. Soc. Sc. Math. Roumanie 49 (2006), 5-11 (cu C.Boboc).
  63. Relative regular objects in categories, Applied Categorical Structures 14 (2006), 567-577 (cu C.Nastasescu, A.Tudorache si L.Daus).
  64. On the dimension of the space of integrals for finite dimensional bialgebras, va aparea in Studia Scientiarum Mathematicarum Hungarica.
  65. Group gradings on M3(k), va aparea in Comm. Algebra (cu C.Boboc).



Actualizat: 31 mai 2007



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