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

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

COD CNCSIS: 1905, contract nr. 538/2009

Descrierea succinta a proiectului de cercetare

Proiectul are doua directii de cercetare. Prima directie de cercetare este dedicata studiului spatiilor Banach de matrici superior triunghiulare infinite, numite matrici analitice precum si a unor operatori de speciali care actioneaza pe ele, drept exemple fiind operatorii Hankel si operatorii de multiplicare Schur. Se are in vedere continuarea studiului spatiilor matriceale analoage spatiilor Bloch si respective Bergman de functii analitice studiu inceput de Nicolae Popa. In plus un rol important in studiul acestor spatii il vor juca multiplicatorii Schur, obtinandu-se noi rezultate fata de studiul clasic al multiplicatorilor Fourier. De asemenea vor fi considetrati operatori Hankel matriciali studiati anterior de V. V Peller si M. Marsalli. Un accent deosebit se va pune pe nuclearitatea acestor operatori si relatia lor cu spatiile Besov de matrici precum si cu un spatiu considerat de Pelczynski si Sukochev. A doua directie de cercetare consta in cautarea unor metode de asociere a unor clase de functii scalare si a unor corespondente intre sisteme de operatori pe spatii Banach astfel incat sa aiba loc o proprietate de transformare a spectrului, analoaga teoremei de transformare a spectrului din cazul calculului functional. In acest context se are in vedere calculul functional al comutatorului sistemelor de operatori si studiul unor clase de operatori analoage bicomutantului sistemelor de operatori in spatii Banach.

Director de proiect

Prof. Dr. Sabac Mihai

Membrii

Cercetator Stiintific gr. I Popa Nicolae
Doctorand Marcoci Anca-Nicoleta
Doctorand Marcoci Liviu-Gabriel

Lucrari publicate in cadrul proiectului

"A new characterization of Bergman-Schatten spaces and a duality result" avand ca autori pe Liviu Gabriel Marcoci, Lars-Erik Persson, Irina Popa si Nicolae Popa in revista cotata ISI Journal of Mathematical Analysis and Applications, vol. 360, Iss. 1, 2009.
"Schur multipliers characterization of a class of infinite matrices", autori Anca Nicoleta Marcoci, Liviu Gabriel Marcoci, Lars-Erik Persson si Nicolae Popa acceptata pentru publicare in revista cotata ISI Czechoslovak Mathematical Journal.
"Commuting systems of bounded operators, factorizations and spectral correspondence", autor Mihai Sabac acceptata in volumul dedicat Conferintei Internationale Operator Theory 22.