Grant no. 88/05.10.2011 CNCSUEFISCDI
Grant no. 88/05.10.2011 of the Romanian National Authority for Scientific Research, CNCSUEFISCDI. Title: ‘Hopf algebras and related topics’
Code of the project: PNIIIDPCE201130039
The team: Prof. Gigel Militaru (the team leader of the project), CS III Sebastian Burciu, CS III Bogdan Ion, AC AnaLoredana Agore (PhD student – PhD since 1/10/2012), AC Costel Gabriel Bontea (PhD student).
Project Summary: Hopf algebras were introduced around 1960 arising from algebraic geometry and algebraic topology. The second important development within this field of study started in 1987 with the appearance of the paper Quantum groups by V. Drinfel’d. The project will be focused on both parts (classic and quantum) of the theory of Hopf algebras and has two corresponding general objective each of them with several open problems. Objective I: New structural results for Hopf algebras. There are four open problems related to this objective. Objective II: Categorical methods in quantum groups. Braided, monoidal and fusion categories. There are five open problems related to the second objective.
Actual annual expenses: 2011 2012 2013 2014 2015 2016
Annual scientific reports (in romanian): RS_2011 RS_2012 Raport_Stiintific_sintetic_2011_2013 RS_2014 RS_2015 rs_final
Annual scientific reports (in english): 2011 2012 RS_2011_2013 2014 SR_en_2015 sr_2016_en en_raport_stiintific_sintetic_final
Published/Accepted papers in ISI journals (the impact factor is given):
The stage 2012:
[1] A.L. Agore, S. Caenepeel, G. Militaru – The center of the category of bimodules and descent data for noncommutative rings, J. Algebra Appl. 11 (2012), 117. (IF: 0.483) Link: http://www.worldscientific.com/doi/abs/10.1142/S0219498812501022?prevSearch=Agore&searchHistoryKey=
[2] G. Militaru – Representable functors for corings, Comm. Algebra 40 (2012), no.5, 17661796. (IF: 0.347) Link: http://www.tandfonline.com/doi/abs/10.1080/00927872.2011.556694?journalCode=lagb20#.UfH4kqz7aM4
[3] A. L. Agore and G. Militaru – Schreier type theorems for bicrossed products, Cent. Eur. J. Math. 10 (2012), no.2, 722739. (IF: 0.440) Link: http://link.springer.com/article/10.2478%2Fs1153301101286
[4] A.L. Agore, S. Caenepeel, G. Militaru – Braidings on the category of bimodules, Azumaya algebras and epimorphisms of rings, Applied Cat. Structures, 22 (2014), 29–42 (IF: 0.600) Link: http://link.springer.com/article/10.1007/s1048501292943
[5] A. L. Agore, C. G. Bontea, G. Militaru – Classifying bicrossed products of Hopf algebras, Algebr. Represent. Theory, 17(2014), 227264 ( IF: 0.595). Link: http://link.springer.com/article/10.1007/s1046801293965
[6] S. Burciu – Subgroups of odd depth – a necessary condition, Czechoslovak Math. J., 63(2013), 10391048 (IF: 0.262) Link: http://link.springer.com/article/10.1007%2Fs1058701300709
[7] A. L. Agore, G. Militaru – Unified products and split extensions of Hopf algebras, Contemporary Math. AMS, Vol. 585 (2013), 115. Link: http://www.ams.org/bookstore/pspdf/conm585toc.pdf
The stage 2013:
[1] S. Burciu, S. Natale – Fusion rules of equivariantizations of fusion categories, Journal of Mathematical Physics, 54(2013), ID: 013511, (IF: 1.291). Link: http://jmp.aip.org/resource/1/jmapaq/v54/i1/p013511_s1?bypassSSO=1
[2] A. L. Agore and G. Militaru – Unified products for Leibniz algebras, Linear Algebra and its Applications, 439 (2013), 26092633, (IF: 0,974) Link: http://www.sciencedirect.com/science/article/pii/S0024379513004722
[3] A. L. Agore, G. Militaru – Classifying complements for Hopf algebras and Lie algebras, Journal of Algebra, 391(2013), 193208 (IF: 0,613) Link: http://www.sciencedirect.com/science/article/pii/S0021869313003268
[4] A. L. Agore, G. Militaru – Extending structures for Lie algebras, Monatshefte für Mathematik, 174(2014), 169193, (IF: 0,616) Link: http://link.springer.com/article/10.1007/s0060501305377
[5] A.L Agore – Coquasitriangular structures for extensions of Hopf algebras, Glasgow Math. J. 55 (2013), 115. (IF: 0.571) Link: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8768821
[6] A. L. Agore, C. G. Bontea, and G. Militaru – Classifying coalgebra split extensions of Hopf algebras, J. Algebra Appl. 12 (2013), 124. (IF: 0.483) Link: http://www.worldscientific.com/doi/abs/10.1142/S0219498812502271?af=R&
[7] A.L. Agore, G. Militaru – Extending structures I: the level of groups, Algebr. Represent. Theory, 17(2014), 831848, (IF: 0.595) Link: http://link.springer.com/article/10.1007/s1046801394204
[8] S. Burciu – Kernels of representations of Drinfel’d doubles of finite groups, Cent. Eur. J. Math., 11(2013), 19001913 (IF: 0.440) Link: http://link.springer.com/article/10.2478%2Fs1153301302985
[9] C. G. Bontea – Classifying bicrossed products of two Sweedler.s Hopf algebras, Czechoslovak Math. J., 64(2014), 419431 (IF: 0.262)
The stage 2014:
[1] V. Chari, B. Ion – BGG reciprocity for current algebras, accepted for publication in Compositio Math, (Article Influence Score: 2,33, IF: 1,18). Link: http://dx.doi.org/10.1112/S0010437X14007908
[2] V. Chari, B. Ion, D. Kus, Weyl modules for the hyperspecial curent algebra, accepted for publication in Int. Math. Res. Notices, (Article Influence Score: 1,55, IF: 1,01). Link: http://dx.doi.org/10.1093/imrn/rnu135
[3] A.L. Agore, Free Poisson Hopf algebras generated by coalgebras, Journal of Mathematical Physics, 55(2014), ID: 083502, 11 pages (IF: 1.291). Link: http://scitation.aip.org/content/aip/journal/jmp/55/8/10.1063/1.4889936
[4] A.L. Agore, Classifying complements for associative algebras, Linear Algebra and its Applications, 446(2014), 345355 (IF: 0,974). Link: http://www.sciencedirect.com/science/article/pii/S0024379514000305
[5] A. L. Agore, C. G. Bontea, and G. Militaru – The classification of all crossed products H_{4} # k[C_{n}], Symmetry Integr. Geom., 10 (2014), 049, 12 pages (IF: 1,071). Link: http://www.emis.de/journals/SIGMA/2014/049/
[6] G. Militaru – The global extension problem, coflag and metabelian Leibniz algebras, Linear and Multilinear Algebra, Vol. 63 (3) (2015), 601621 (IF: 0,727) Link: http://www.tandfonline.com/doi/full/10.1080/03081087.2014.891587
[7] A.L. Agore, G. Militaru – Bicrossed products, matched pair deformations and the factorization index for Lie algebras – Symmetry Integr. Geom., 10(2014), 065, 16 pages (IF: 1,071). Link: http://www.emis.de/journals/SIGMA/2014/065/
[8] S. Burciu – On coideal subalgebras of abelian cocentral extensions and a generalization of Wall’s conjecture, J. Algebra Appl. Vol. 14, No. 2 (2015), 1550021 (IF: 0.483) Link: http://www.worldscientific.com/doi/abs/10.1142/S0219498815500218?src=recsys&
The stage 2015:
[1] A. L. Agore, G. Militaru – Classifying complements for groups. Applications, Annales de l’Insitut Fourier, 65(2015), 1349 – 1365 (Article Influence Score: 1,24, IF: 0,66). Link: http://aif.cedram.org/aifbin/item?id=AIF_2015__65_3_1349_0
[2] A. L. Agore, G. Militaru – Extending structures, Galois groups and supersolvable associative algebras, accepted for publication in Monatshefte für Mathematik, (IF: 0,647). Link: http://link.springer.com/article/10.1007/s0060501508148
[3] A.L. Agore, G. Militaru – The global extension problem, crossed products and coflag noncommutative Poisson algebras, Journal of Algebra, 426(2015), 131 (IF: 0,59) Link: http://dx.doi.org/10.1016/j.jalgebra.2014.12.007
[4] A. L. Agore, G. Militaru – On a type of commutative algebras, Linear Algebra and its Applications, 485(2015), 222249 (IF: 0,939). Link: http://www.sciencedirect.com/science/article/pii/S0024379515004498
[5] A.L. Agore, G. Militaru, Ito’s theorem and metabelian Leibniz algebras, Linear and Multilinear Algebra, 63 (2015), 2187–2199. (IF: 0,73) Link: http://dx.doi.org/10.1080/03081087.2014.992771
The stage 2016:
[1] A.L. Agore, G. Militaru, Jacobi and Poisson algebras, Journal of Noncommutative Geometry, 9 (2015), 12951342 (Article Influence Score: 1,22, IF: 0,94). Link: http://www.emsph.org/journals/show_abstract.php?issn=16616952&vol=9&iss=4&rank=10
[2] A.L. Agore, The maximal dimension of unital subalgebras of the matrix algebra, accepted for publications in Forum Math. (IF: 0,96) : DOI: 10.1515/forum20150241 Link: https://www.degruyter.com/view/j/form.aheadofprint/forum20150241/forum20150241.xml
[3] G. Militaru – Metabelian associative algebras, accepted for publication in Bulletin of the Malaysian Mathematical Sciences Society, DOI: 10.1007/s4084001501576 (IF: 0,64). Link: http://link.springer.com/article/10.1007/s4084001501576
[4] A. L. Agore, G. Militaru – Hochschild products and global nonabelian cohomology for algebras. Applications, acceptated for publication in Journal of Pure and Applied Algebra, 221 (2017), 366392 (IF: 0.66) Link: http://www.sciencedirect.com/science/article/pii/S0022404916300846
Dissemination of the scientific results. Talks given at international conferences:
The stage 2011:
[C1] G. Militaru – Split extensions of Hopf Algebras, Algebra Geometry Mathematical Physics, Mulhouse,
Octomber 2011.
The stage 2012:
[C1] G. Militaru – Classifying bicrossed products of quantum groups, Algebra Geometry Mathematical Physics, Brno, september 2012.
[C2] A. L. Agore – Deformations and descent type theory for Hopf algebras, Algebra Geometry Mathematical Physics, Brno, September 2012.
[C3] C. Bontea – Classifying crossed product of quantum groups,Algebra Geometry Mathematical Physics(AGMP), Brno, September 2012.
[C4] A.L. Agore – Bicrossed descent theory of exact factorizations and the number of types of groups of finite order , Groups and their actions, Bedlewo, July 2012
[C5] G. Militaru – Extending structures: the level of groups, Groups and their actions, Bedlewo, July 2012.
[C6] G. Militaru – Classifying bicrossed products. Deformations and descent type theory for quantum groups, Hopf Algebra Workshop, Brussel VUB, 19 March 19, 2012.
The stage 2013:
[C7] A.L. Agore – Classifying exact factorizations of a group through a given subgroup and the number of types of groups of finite order, 2^{nd} Biennial Groups Theory Conference, Dogus University, Istanbul, February 2013.
[C8] G. Militaru – The Extending Structures Problem, 2^{nd} Biennial Groups Theory Conference, Dogus University, Istanbul, February, 2013
[C9] A.L. Agore – The factorization problem for Lie algebras, International workshop Lie theory and its applications, Varna, Bulgaria, June 2013.
[C10] G. Militaru – Extending structures for Lie algebras, International workshop Lie theory and its applications, Varna, Bulgaria, June 2013.
[C11] A.L. Agore – Bicrossed products of Hopf algebras, Workshop for young researchers, Constanta, Romania, May 2013.
[C12] A.L. Agore – Exact factorizations for Hopf algebras. Applications, Joint international meeting of AMS and RMS , AlbaIulia, Romania, June 2013.
[C13] G. Militaru – The extension problem for Hopf algebras, Joint international meeting of AMS and RMS, AlbaIulia, Romania, June 2013.
[C14] G. Militaru – The extending structures for algebras, Workshop ‘Rings, categories and Hopf algebras’, Bucharest, May 2013.
[C15] G. Militaru – Quasitriangular algebras, braidings on bimodules and central simple algebras, International Conference ”Some Trends in Algebras”, September 39, 2013, Prague.
[C16] A.L. Agore – Extending structures for algebras, International Conference ”Some Trends in Algebras”, September 39, 2013, Prague.
[C17] A.L. Agore – Classifying complements for Hopf algebras, Lie algebras and groups, Workshop ‘Rings, categories and Hopf algebras’, Bucharest, May 2013.
[C18] C.G. Bontea – The factorization problem for Hopf algebras, Workshop ‘Rings, categories and Hopf algebras’, Bucharest, May 2013.
[C19] S. Burciu – Kernels of representations and coideal subalgebras of Hopf algebras Workshop “Rings, Categories and Hopf Algebras”, May 1819, 2013, Bucharest.
The stage 2014:
[C1] A. Agore – The extending structures problem for Lie algebras, XXIInd International Conference on Integrable Systems and Quantum symmetries (ISQS22), Prague, June 23 June 29, 2014.
[C2] A. Agore – Classifying split extensions of quantum groups – 30th International Colloquium on Group Theoretical Methods in Physics, Ghent University, Belgium, July 1418, 2014
[C3] G. Militaru – The global extension problem, crossed products and coflag noncommutative Poisson algebras, XXIInd International Conference on Integrable Systems and Quantum symmetries (ISQS22), Prague, June 23 June 29, 2014.
The stage 2015:
[C1] G. Militaru – Jacobi and Poisson algebras, The Second International Conference on Mathematics and Statistics, AUSICMS ‘15, American Univ. Sharjah, April 2 – 5, 2015.
[C2] A. L. Agore – Hochschild products and global nonabelian cohomology for algebras, The Second International Conference on Mathematics and Statistics, AUSICMS ‘15, American Univ. Sharjah, April 2 – 5, 2015.
[C3] A. L. Agore – On the classification of bicrossed products of Hopf algebras, New trends in Hopf algebras and tensor categories, Palace of the Academies, Brussels, June 25, 2015
[C4] G. Militaru – Jacobi and Poisson algebras, New trends in Hopf algebras and tensor categories, Palace of the Academies, Brussels, June 25, 2015
[C5] G. Militaru – The factorization problem and related questions, The Eighth Congress of Romanian Mahtematicians, Iasi, June 26 – July 1. 2015
[C6] A. L. Agore – Jacobi and Poisson algebras, The Eighth Congress of Romanian Mahtematicians, Iasi, June 26 – July 1. 2015
[C7] A.L. Agore – The factorization index for finite groups – The Young Reserchers in Mathematics Conference, University of Oxford, August 1720, 2015.
[C8] A.L. Agore – Galois groups and group actions on Lie algebras – Ferrara Algebra Workshop, University of Ferrara, Italy – September 1718, 2015.
[C9] G. Militaru – Leibniz algebras – Ferrara Algebra Workshop, University of Ferrara, Italy – September 1718, 2015.
The stage 2016:
[C1] A. L. Agore – Galois theory for Lie algebras, Workshop on Hopf Algebras and Related Topics, University of Turin, 2122 January, 2016
[C2] G. Militaru – Leibniz algebras, 20th Conference of the International Linear Algebra Society, Leuven, 1114 July, 2016
[C3] G. Militaru – Galois groups and groups actions on Lie algebras, 7th European Congress of Mathematics, Berlin, 1822 July, 2016
[C4] A. L. Agore – Bicrossed descent theory for groups. Applications, 7th European Congress of Mathematics, Berlin, 1822 July, 2016
Update: 05.10.2016
Clasificarea algebrelor Lie de dimensiune mica
O problema clasica, veche si grea, care revine mereu in actualitate. Citeva linkuri foarte utile si care trimit la alte referinte sunt cele doua de mai jos. Inteleg ca sau tot facut clasificari (pana la dimnesiune 7) in multe articole, ca sau tot comis erori si scapari.
http://terrytao.wordpress.com/tag/liealgebras/
http://mathoverflow.net/questions/21114/lowdimensionalnilpotentliealgebras
si o carte http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf

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