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Descriere succinta a proiectului de cercetare

In acest proiect ne propunem sa continuam studiul algebrelor Hopf si al unor structuri algebrice strans legate de acestea, pe urmatoarele directii de cercetare:

1. Coactiuni ale unor clase de algebre Hopf pe anumite algebre;
2. Structuri braided monoidale versus bimonade monoidale;
3. Proprietati omologice ale algebrelor de incidenta;
4. Produse incrucisate;
5. Coomologie ciclica pentru algebre;
6. Structuri combinatorice cu aplicatii la algebre si coalgebre.

Director de proiect

Prof.dr. Sorin Dascalescu, Facultatea de Matematica si Informatica a Universitatii din Bucuresti.

Cercetare sprijinita financiar de acest grant:

1. S. Dascalescu, M. Iovanov si C. Nastasescu, Quiver Algebras, Path Coalgebras and co-reflexivity, Pacific Journal of Mathematics 262 (2013), 49-79.
2. M. Barascu si S. Dascalescu, Good gradings on upper block triangular matrix algebras, Comm. Algebra 41 (2013), 4290-4298.
3. S. Dascalescu, S. Predut si L. Van Wyk, Jordan isomorphisms of generalized structural matrix rings, Linear and Multilinear Algebra Vol. 61, No. 3, martie 2013, 369-376.
4. S. Dascalescu, M. C. Iovanov, S. Predut, Frobenius structural matrix algebras, Linear Alg. Appl. 439 (2013), 3166-3172.
5. D. Joita, C. Nastasescu si L. Nastasescu, Recollement of Grothendieck categories. Applications to schemes, Bull. Math. Soc. Sci. Math. Roum. 56 (104), no. 1, 2013, 109-116.
6. A. Petrescu-Nita si D. M. Staic, Symmetry group of two special types of carbon nanotori, Acta Crystallographica Section A, Volume 69, Part 4, 2013, 435-439.
7. M. Barascu, Good Z_p^2xZ_pxZ_p-gradings on matrix algebras, Annals of the University of Bucharest (Mathematical Series), 4(2) (2013), 425-431.
8. M. Iovanov, Complete path algebras and rationals modules, Bull. Math. Soc. Sci. Math. Roum. 56 (2013), 349-364.
9. F. Panaite, Equivalent crossed products and cross product bialgebras, Comm. Algebra 42(5)(2014), 1937-1952.
10. F. Panaite, Iterated crossed products, J. Algebra Appl. 13(7) (2014), 1450036 (14 p.).
11. S. Dascalescu, C. Nastasescu, L. Nastasescu, Frobenius algebras of corepresentations and group-graded vector spaces, J. Algebra 406 (2014), 226-250.
12. A. Makhlouf, F. Panaite, Yetter-Drinfeld modules for Hom-bialgebras, J. Math. Phys. 55, 013501 (2014).
13. S. Dascalescu, M. C. Iovanov, Semiperfect and coreflexive coalgebras, Forum Mathematicum 27(5) (2015), 2587-2607.
14. A. Makhlouf, F. Panaite, Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra, J. Algebra 441 (2015), 314-343.
15. M. Iovanov, Triangular matrix coalgebras and applications, Linear and Multilinear Algebra 63(1) (2015), 46-67.
16. M. Hughes, D. M. Staic, Xie Xiangdong, Classification of a class of nonrigid Carnot groups, Journal of Lie Theory 25 (2015), 717-732.
17. D. M. Staic, A. Stancu, Operations on the Secondary Hochschild Cohomology, Homology, Homotopy and Applications 17 (2015), 129-146.
18. D. Bulacu si B. Torrecillas, On Frobenius and separable algebra extensions in monoidal categories. Applications to wreaths, Journal of Noncommutative Geometry 9(3) (2015), 707-774.
19. G. Graziani, A. Makhlouf, C. Menini, F. Panaite, BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras, Symmetry, Integrability Geom. Methods Appl. (SIGMA) 11 (2015), 086, 34 pagini.
20. C. Boboc. S. Dascalescu, L. van Wyk, Jordan isomorphisms of 2-torsionfree triangular rings, Linear Multilinear algebra 64(2) (2016), 290-296.
21. L. Daus, F. Panaite, A new way to iterate Brzezinski crossed products, Colloq. Math. 142(1) (2016), 51-60.
22. J. Dello, F. Panaite, F. Van Oystaeyen, Y. Zhang, Structure theorems for bicomodule algebras over quasi-Hopfalgebras, Comm. Algebra 44 (2016), 4609-4636.
23. A. Makhlouf, F. Panaite, Twisting operators, twisted tensor products and smash products for Hom-associative algebras, Glasgow Math. J. 58(3) (2016), 513-538.
24. D. Stefan, C. Vay, The cohomology ring of the 12-dimensional Fomin-Kirillov algebra, Advances in Mathematics 291 (2016), 584-620.
25. D. M. Staic, Secondary Hochschild homology, Algebras and Representation theory 19(1) (2016), 47-56.
26. A. Manea, D. S tefan, Further properties of Koszul pairs and applications, Symmetry Integrability and Geometry-Methods and Applications 12 (2016), Article Number:092.
27. Bruce R. Corrigan-Salter, Mihai D. Staic, Higher-order and secondary Hochschild cohomology. C. R. Math. Acad. Sci. Paris 354 (2016), no. 11, 1049-1054.
28. S. Dascalescu, C. Nastasescu, L. Nstasescu, Symmetric algebras in categories of corepresentations and smash products, J. Algebra 465 (2016), 62-80.
29. M. Iovanov, Z. Mesyan, M. Reyes, Infinite-dimensional diagonalization and semisimplicity, acceptat spre publicare in Israel Journal of Mathematics.
30. P. Jara, J. L. Pena,D. Stefan, Koszul pairs. Applications, acceptat spre publicare in Journal of Noncommutative Geometry.
31. D. Bulacu, S. Caenepeel , B.Torrecillas, Frobenius and separable functors for the category of generalized entwined modules. Applications, trimisa spre publicare la Trans. Amer. Math. Soc.
32. M. Barascu, Counting good gradings on upper block triangular matrix algebras, in curs de revizuire.
33. D. Bulacu, B. Torrecillas, Galois theory and cleft extensions for monoidal cowreaths. Applications, trimis spre publicare la Proc. London Math. Soc.
34. A. Manea, D. Stefan, On Koszulity of finite graded posets, acceptat pentru publicare la Journal of Algebra and Its Applications.
35. F. Panaite, F. Van Oystaeyen, Twisted algebras and Rota-Baxter type operators, acceptat la J. Algebra Appl.
36. Jacob Laubacher, Mihai D. Staic, Alin Stancu, Bar Simplicial Modules and Secondary Cyclic (Co)homology, in stadiu avansat de finalizare.

Durata proiectului:

01.01.2012-31.12.2016

Buget:

500.000,00 RON/2012
225.745,43 RON/2013
250.000 RON/2014
169.152 RON/2015
355.102,57 RON/2016

Raportare 2012:

• Raport stiintific
• Deviz postcalcul

Raportare 2013:

• Raport stiintific
• Deviz postcalcul

Contractare/Raportare 2014:

• Raport stiintific
• Plan de realizare a proiectului
• Deviz cadru antecalcul

Contractare/Raportare 2015:

• Raport stiintific
• Plan de realizare a proiectului
• Deviz cadru antecalcul
• Deviz postalcul

Contractare/Raportare 2016:

• Raport stiintific
• Plan de realizare a proiectului
• Deviz cadru antecalcul