Florin Panaite

Personal

Born: 24-10-1970, Bucharest, Romania

Citizenship: Romanian

Professional adress:

Institute of Mathematics of the Romanian Academy,
P.O.Box 1-764, RO-014700, Bucharest, Romania
e-mail: Florin(dot)Panaite(at)imar(dot)ro

Academic rank:

Senior Researcher I (CS I), Institute of Mathematics of the Romanian Academy (IMAR)

Languages:

• Romanian-mother tongue
• English-fluent
• French-good
• Spanish-reading

Educational history:

• High School ''Sfantul Sava'', Bucharest, 1985-1989
• University Degree in Mathematics, University of Bucharest, 1995
• Master of Science in Algebra, University of Bucharest, 1996
• Ph.D. in Mathematics, University of Bucharest, 1999, with the thesis "Algebras and coalgebras with applications to quantum groups", advisor Prof. Dr. C. Nastasescu

Awards:

The prize "Gheorghe Lazar" of the Romanian Academy for 1999 (awarded in 2001)

Research visits abroad:

• 1996: 3 months at University of Antwerp, UIA, Belgium, with a TEMPUS grant
• 1998: 10 months at University of Antwerp, UIA, Belgium, in the framework of the cooperation project Hopf algebras and (co) Galois theory supported by the Flemish and Romanian Ministries of Research
• 2001: 1 month at Ecole Polytechnique Federale de Lausanne, Switzerland, supported by the programme SCOPES
• 2003: 2 months at University of Antwerp, Belgium, supported by the programmes EURROMMAT of IMAR and Hopf algebras in Algebra, Topology, Geometry and Physics financed by the Flemish and Romanian Ministries of Research
• 2004: 6 months at University of Almeria, Spain, supported by a NATO postdoctoral fellowship offered by the Spanish Ministry of Science and Technology
• 2005-2006: 9 months at University of Antwerp, Belgium, supported by a Marie Curie postdoctoral fellowship within the RTN programme LIEGRITS and by the project New techniques in Hopf algebras and graded ring theory financed by the Romanian and Flemish governments
• 2006: 4 months at the Centre for Mathematics of the University of Coimbra (CMUC), Portugal, supported by a postdoctoral fellowship offered by CMUC
• 2007: 2 weeks at University of Granada, Spain, supported by a grant from the Spanish Ministry of Science and Technology
• 2007-2008: 12 months at University of Antwerp, Belgium, supported by a postdoctoral fellowship offered by FWO (Flemish Foundation for Scientific Research)
• 2011: 6 weeks at the Centre for Mathematics of the University of Coimbra (CMUC), Portugal, supported by the CNCSIS project ''Hopf algebras, cyclic homology and monoidal categories'', contract nr. 560/2009, CNCSIS code ID69
• 2012: 1 month at University of Hasselt, Belgium, supported by the CNCS project ''Hopf algebras in category theory, representation theory and combinatorics'', contract nr. 253/2011, project nr. PN-II-ID-PCE-2011-3-0635
• 2012: 2 weeks at University of Antwerp, Belgium, supported by the CNCS project ''Hopf algebras in category theory, representation theory and combinatorics'', contract nr. 253/2011, project nr. PN-II-ID-PCE-2011-3-0635
• 2012: 1 week at University of Almeria, Spain, supported by the CNCS project ''Hopf algebras in category theory, representation theory and combinatorics'', contract nr. 253/2011, project nr. PN-II-ID-PCE-2011-3-0635
• 2013: 1 month at University of Antwerp, Belgium, supported by a grant from FWO (Flemish Foundation for Scientific Research) within the research project ''Equivariant Brauer groups and Galois deformations''
• 2013: 1 month at Universite de Haute Alsace (UHA), Mulhouse, France, supported by the CNCS project ''Hopf algebras in category theory, representation theory and combinatorics'', contract nr. 253/2011, project nr. PN-II-ID-PCE-2011-3-0635
• 2013: 1 week at United Arab Emirates University, Al Ain (UAE), supported by UAEU and by the CNCS project ''Hopf algebras in category theory, representation theory and combinatorics'', contract nr. 253/2011, project nr. PN-II-ID-PCE-2011-3-0635
• 2014: 1 month at Universite de Haute Alsace (UHA), Mulhouse, France, supported by a grant offered by UHA
• 2014: 1 month at Erwin Schrodinger Institute, Vienna, Austria, supported by the CNCS project ''Hopf algebras in category theory, representation theory and combinatorics'', contract nr. 253/2011, project nr. PN-II-ID-PCE-2011-3-0635
• 2014: 1 month at University of Ferrara, Italy, supported by a grant from INdAM (Instituto Nazionale di Alta Matematica)
• 2014: 1 month at University of Antwerp, Belgium, supported by a grant from FWO (Flemish Foundation for Scientific Research) within the research project ''Equivariant Brauer groups and Galois deformations''
• 2015: 1 month at University of Antwerp, Belgium, supported by a grant from FWO (Flemish Foundation for Scientific Research) within the research project ''Equivariant Brauer groups and Galois deformations''
• 2015: 10 days at University of Ferrara, Italy, supported by the CNCS project ''Hopf algebras in category theory, representation theory and combinatorics'', contract nr. 253/2011, project nr. PN-II-ID-PCE-2011-3-0635
• 2017: 1 month at Universite de Haute Alsace (UHA), Mulhouse, France, supported by a grant offered by UHA
• 2017: 1 month at University of Ferrara, Italy, supported by a grant from INdAM (Instituto Nazionale di Alta Matematica)

Research fields:

Quantum algebra (Hopf algebras, quantum groups)

Research summary:

My field of research is the theory of Hopf algebras and quantum groups, including extensions of these concepts (quasi-Hopf algebras, quantum groupoids, Hom-bialgebras etc). In my research I have treated various aspects of the theory, such as: quasitriangular structures, ribbon and charmed elements, monoidal, braided and ribbon categories, links with braid groups, Clifford algebras, octonions and Cayley-Dickson algebras, various kinds of crossed products (smash products and biproducts, double crossed products, diagonal crossed products, L-R-smash products, twisted tensor products of algebras, Brzezinski crossed products), twistings of algebras and Rota-Baxter type operators, integrals and Maschke-type theorems, quantum traces and dimensions, actions and coactions, cleft extensions, the study of some classes of pointed Hopf algebras, (anti) Yetter-Drinfeld modules and Hopf (bi)modules, the quantum Yang-Baxter equation and the pentagonal equation, vertex groups, the Drinfeld double and the Heisenberg double, combinatorial and homological aspects, extensions, deformations etc.

See the list of publications.

Talks at Conferences:

• ''Hopf Algebras and Quantum Groups'', Brussels (Belgium), June 1998
• ''Operator Algebras and Mathematical Physics'', Constanta (Romania), July 2001
• ''Hopf Algebras in Noncommutative Geometry and Physics'', Brussels (Belgium), May 2002
• ''Nonassociative Algebras and Related Topics'', Coimbra (Portugal), July 2011
• ''Algebra, Geometry, Mathematical Physics VII'', Mulhouse (France), October 2011
• ''Rings, Categories and Hopf Algebras. A conference in honour of Prof. Constantin Nastasescu'', Bucharest (Romania), May 2013
• Anniversary Conference: ''Faculty of Sciences-150 years'', Bucharest (Romania), August 2013
• The Eighth Congress of Romanian Mathematicians, Iasi (Romania), June 2015
• ''Ferrara Algebra Workshop. A conference in honour of Prof. Claudia Menini'', Ferrara (Italy), September 2015
• ''The First Romanian-Turkish Mathematical Colloquium'', Constanta (Romania), October 2015
• ''Algebra and Group Theory. A conference in honour of Prof. Otto Kegel'', Mulhouse (France), October 2015

Talks at Seminars, Workshops etc:

• ARTS (Antwerp Ring Theory Seminar), University of Antwerp, Belgium, May 1998, May 2006
• SANO (Seminario de Algebra No Conmutativa), University of Granada, Spain, April 2004, November 2007
• Workshop "New techniques in Hopf algebras and graded ring theory", Vrije Universiteit Brussels, Belgium, September 2005
• Mini-course (5 hours) "General twisted algebras" during the Socrates Intensive Program "Geometric and Algebraic Methods with Applications in Physics", University of Antwerp, Belgium, September 2007
• Seminar Hopf-Galois, Hasselt University, Belgium, February 2008
• SAAM (Seminario de Algebra y Analysis Matematico), University of Almeria, Spain, November 2012
• Seminar of the Department of Mathematics, United Arab Emirates University, Al Ain (UAE), November 2013
• Seminaire ''Georges Reeb'' (Algebre et Geometrie Differentielle), Universite de Haute Alsace (UHA), Mulhouse, France, March 2014, June 2017
• Algebra Seminar, University of Ferrara, Italy, September 2014
• Algebra Seminar, University of Padova, Italy, October 2014
• Workshop ''Hom-Algebras'', Monastir, Tunisia, October 2014

Other Conferences, Workshops and Summer Schools attended:

• International Conference on Representation Theory of Groups, Algebras and Orders, Constanta (Romania), September 1995
• AMS-BeNeLux Congres, Antwerp, May 1996
• Summer School on Representation Theory of Algebras, Finite and Reductive Groups, Cluj-Napoca (Romania), September 1997
• TMR Workshop on Noncommutative Algebra, Antwerp, June 1998
• TMR Workshop on Differential Operators and Quantum Algebras, Reims, November 1998
• Summer School and Workshop on Decomposition Numbers and Character Formulae for Lie Algebras, Algebraic Groups and Quantum Groups, Blaubeuren (Germany), May 1999
• Euroconference and Workshop on Algebra and Representation Theory, Constanta (Romania), August 2000
• Summer School on Geometry of Quiver Representations and Preprojective Algebras, Isle of Thorns (Sussex, UK), September 2000

List of publications:

• Ribbon and charmed elements for quasitriangular Hopf algebras, Comm. Algebra 25 (3), 973-977 (1997).
• When is the category of comodules a braided tensor category? Rev. Roum. Math. Pures Appl. 42 (1-2), 107-119 (1997) (with D. Stefan).
• An example of quantum commutativity: the generalized Clifford algebra, Stud. Cerc. Mat. 49 (3-4), 225-229 (1997).
• Coalgebra deformations of bialgebras by Harrison cocycles, Bull. Belg. Math. Soc. 4 (5), 647-671 (1997) (with S. Caenepeel, S. Dascalescu, G. Militaru).
• A Maschke-type theorem for quasi-Hopf algebras, in "Rings, Hopf algebras and Brauer groups" (eds. S. Caenepeel and A. Verschoren), 201-207, Lecture Notes in Pure and Appl. Math. 197, Marcel Dekker, New York (1998).
• A generalization of the quasi-Hopf algebra D^{\omega}(G), Comm. Algebra 26 (12), 4125-4141 (1998) (with D. Bulacu).
• External homogenization for Hopf algebras, Algebr. Represent. Theory 2 (3), 211-226 (1999) (with C. Nastasescu and F. Van Oystaeyen).
• Equivalence of crossed coproducts, Bull. Belg. Math. Soc. 6 (2), 259-278 (1999).
• Quasitriangular structures for some pointed Hopf algebras of dimension 2^n, Comm. Algebra 27 (10), 4929-4942 (1999) (with F. Van Oystaeyen).
• Quantum traces and quantum dimensions for quasi-Hopf algebras, Comm. Algebra 27 (12), 6103-6122 (1999) (with D. Bulacu and F. Van Oystaeyen).
• Clifford-type algebras as cleft extensions for some pointed Hopf algebras, Comm. Algebra 28 (2), 585-600 (2000) (with F. Van Oystaeyen).
• Quasi-Hopf algebras and the centre of a tensor category, in "Hopf algebras and quantum groups" (eds. S. Caenepeel and F. Van Oystaeyen), 221-235, Lecture Notes in Pure and Appl. Math. 209, Marcel Dekker, New York (2000) (with F. Van Oystaeyen).
• Quasi-Hopf algebra actions and smash products, Comm. Algebra 28 (2), 631-651 (2000) (with D. Bulacu and F. Van Oystaeyen).
• Existence of integrals for finite dimensional quasi-Hopf algebras, Bull. Belg. Math. Soc. 7 (2), 261-264 (2000) (with F. Van Oystaeyen).
• Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees, Lett. Math. Phys. 51 (3), 211-219 (2000).
• Deformation cohomology for Yetter-Drinfeld modules and Hopf (bi)modules, Comm. Algebra 30 (1), 331-345 (2002) (with D. Stefan).
• Hopf bimodules are modules over a diagonal crossed product algebra, Comm. Algebra 30 (8), 4049-4058 (2002).
• Quasi-Hopf algebras and representations of octonions and other quasialgebras, J. Math. Phys. 45 (10), 3912-3929 (2004) (with F. Van Oystaeyen).
• More properties of Yetter-Drinfeld modules over quasi-Hopf algebras, in ''Hopf algebras in noncommutative geometry and physics'' (eds. S. Caenepeel and F. Van Oystaeyen), 89-112, Lecture Notes in Pure and Appl. Math. 239, Marcel Dekker, New York (2005) (with D. Bulacu and S. Caenepeel).
• Yetter-Drinfeld categories for quasi-Hopf algebras, Comm. Algebra 34 (1), 1-35 (2006) (with D. Bulacu and S. Caenepeel).
• Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications, Comm. Math. Phys. 266 (2), 355-399 (2006) (with D. Bulacu and F. Van Oystaeyen).
• Some bialgebroids constructed by Kadison and Connes-Moscovici are isomorphic, Appl. Categor. Structures 14 (5-6), 627-632 (2006) (with F. Van Oystaeyen).
• General twisting of algebras, Adv. Math. 212 (1), 315-337 (2007) (with J. Lopez and F. Van Oystaeyen).
• Extending lazy 2-cocycles on Hopf algebras and lifting projective representations afforded by them, J. Algebra 313 (2), 695-723 (2007) (with J. Cuadra).
• A structure theorem for quasi-Hopf comodule algebras, Proc. Amer. Math. Soc. 135 (6), 1669-1677 (2007) (with F. Van Oystaeyen).
• L-R-smash product for (quasi) Hopf algebras, J. Algebra 309 (1), 168-191 (2007) (with F. Van Oystaeyen).
• On some classes of lazy cocycles and categorical structures, J. Pure Appl. Algebra 209 (3), 687-701 (2007) (with M. D. Staic and F. Van Oystaeyen).
• Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category, Israel J. Math. 158 (1), 349-366 (2007) (with M. D. Staic).
• Doubles of (quasi) Hopf algebras and some examples of quantum groupoids and vertex groups related to them, in "Hopf algebras and generalizations" (eds. L. H. Kauffman, D. E. Radford and F. J. O. Souza), 91-115, Contemporary Math. 441, Amer. Math. Soc. (2007).
• Invariance under twisting, in "New techniques in Hopf algebras and graded ring theory" (eds. S. Caenepeel and F. Van Oystaeyen), 85-104, Royal Flemish Academy, Belgium (2007) (with P. Jara, J. Lopez and F. Van Oystaeyen).
• On iterated twisted tensor products of algebras, Internat. J. Math. 19 (9), 1053-1101 (2008) (with P. Jara, J. Lopez and F. Van Oystaeyen).
• Quasialgebra tensor products and smash products, in "Lie theory and its applications in physics VII" (eds. H.-D. Doebner and V. K. Dobrev), 466-469, Heron Press, Sofia (2008) (with H. Albuquerque).
• On quasi-Hopf smash products and twisted tensor products of quasialgebras, Algebr. Represent. Theory 12 (2-5), 199-234 (2009) (with H. Albuquerque).
• A quotient of the braid group related to pseudosymmetric braided categories, Pacific J. Math. 244 (1), 155-167 (2010) (with M. D. Staic).
• Pseudosymmetric braidings, twines and twisted algebras, J. Pure Appl. Algebra 214 (6), 867-884 (2010) (with M. D. Staic and F. Van Oystaeyen).
• L-R-smash biproducts, double biproducts and a braided category of Yetter-Drinfeld-Long bimodules, Rocky Mount. J. Math 40 (6), 2013-2024 (2010) (with F. Van Oystaeyen).
• Alternative twisted tensor products and Cayley algebras, Comm. Algebra 39 (2), 686-700 (2011) (with H. Albuquerque).
• Quasi-elementary H-Azumaya algebras arising from generalized (anti) Yetter-Drinfeld modules, Appl. Categor. Structures 19 (5), 803-820 (2011) (with F. Van Oystaeyen).
• Invariance under twisting for crossed products, Proc. Amer. Math. Soc. 140 (3), 755-763 (2012).
• More examples of invariance under twisting, Czech. Math. J. 62 (1), 187-195 (2012).
• Some (Hopf) algebraic properties of circulant matrices, Algebra Discrete Math. 13 (1), 1-17 (2012) (with H. Albuquerque).
• More examples of pseudosymmetric braided categories, J. Algebra Appl. 12 (4) (2013), 1250186 (21 pages) (with M. D. Staic).
• L-R-smash products and L-R-twisted tensor products of algebras, Algebra Colloq. 21 (1), 129-146 (2014) (with M. Ciungu).
• Yetter-Drinfeld modules for Hom-bialgebras, J. Math. Phys. 55, 013501 (2014) (17 pages) (with A. Makhlouf).
• Equivalent crossed products and cross product bialgebras, Comm. Algebra 42 (5), 1937-1952 (2014).
• Iterated crossed products, J. Algebra Appl. 13 (7) (2014), 1450036 (14 pages).
• BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras, Symmetry, Integrability Geom. Methods Appl. (SIGMA) 11 (2015), 086, 34 pages (with G. Graziani, A. Makhlouf and C. Menini).
• Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra, J. Algebra 441, 314-343 (2015) (with A. Makhlouf).
• A new way to iterate Brzezinski crossed products, Colloq. Math. 142(1), 51-60 (2016) (with L. Daus).
• Twisting operators, twisted tensor products and smash products for Hom-associative algebras, Glasgow Math. J. 58 (3), 513-538 (2016) (with A. Makhlouf).
• Structure theorems for bicomodule algebras over quasi-Hopf algebras, weak Hopf algebras and braided Hopf algebras, Comm. Algebra 44 (11), 4609-4636 (2016) (with J. Dello, F. Van Oystaeyen and Y. Zhang).
• Twisted algebras and Rota-Baxter type operators, J. Algebra Appl. 16 (4) (2017), 1750079 (18 pages) (with F. Van Oystaeyen).
• Hom-tensor categories and the Hom-Yang-Baxter equation, arXiv:math.QA/1702.08475 (with P. Schrader and M. D. Staic).
• Rota-Baxter operators on BiHom-associative algebras and related structures, arXiv:math.QA/1703.07275 (with L. Liu, A. Makhlouf and C. Menini).
• BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota-Baxter operators on BiHom-Lie algebras, arXiv:math.QA/1706.00474 (with L. Liu, A. Makhlouf and C. Menini).
• {sigma, tau}-Rota-Baxter operators, infinitesimal Hom-bialgebras and the associative (Bi)Hom-Yang-Baxter equation, arXiv:math.QA/1802/07287 (with L. Liu, A. Makhlouf and C. Menini).