Brief description of the project

The project is concerned to several research topics in noncommutative algebra: Hopf algebras and quasi-Hopf algebras, corings, braided monoidal categories, entwined modules, involutive functors, binary trees. Briefly, the main aims of the project are the following:

• Some classification results for hopf algebras and quasi-hopf algebras.
• The study of strongly involutive functors on abstract categories, and some general theorems of moore-penrose type.
• A study of corings in braided monoidal categories and their connections with the entwining structures.
• A systematic study of the categories of entwined modules in braided monoidal categories, with a special emphasis on their description as a category of comodules over a coring or as a category of modules over an algebra in a monoidal category.
• Unifying results about hopf modules over several types of generalized hopf algebras by using the language and techniques of braided monoidal categories.
• Finding necessary and sufficient conditions such that the smash algebra structure induced by a local braiding and the smash coalgebra structure (induced also by a local braiding) endow a certain object with a bialgebra, respectively a hopf algebra, structure within the braided monoidal category.
• k-theory for coalgebras and hopf algebras.
• An approach to some combinatorial problems related to binary trees by using quantum algebraic structures.

A central aim of the project is the integration of the two young researchers in a team working on actual problems, where they could find enough topics to complete the phd thesis by the end of the project. The project also creates a network of external mobilities related to the scientific objectives, and the young researchers will have a consistent profit from this.

Senior researchers

• Constantin Nastasescu
• Sorin Dascalescu
• Daniel Bulacu

Senior researchers

• Gefry Barad
• Bogdan Nicolae Toader

Published papers

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, to appear in Bull. Math. Soc. Sci. Math. Roumanie, 2009.

Reports (Romanian)

• General evaluation: 2007, 2008, 2009, 2010
• Scientific evaluation: 2007, 2008, 2009, 2010
• Monitorisation 06.05.2010