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Research Grant PN-II-RU-TE-2009, project ID_303, 28.07.2010-27.07.2013, financed by CNCSIS

"Group Algebras and Ringel-Hall Algebras"

Faculty of Economics and Business Administration, Babes-Bolyai University, Cluj-Napoca
Research team
Assoc. Prof. Dr. Gabriela Olteanu (project manager)
Assoc. Prof. Dr. Csaba Szanto
Teaching assist. Dr. Stefan Suteu Szollosi
Brief presentation of the project

The project goals are to provide a reseach framework for its members and the formation of the involved young researcher, to find and introduce new directions and methods of research. We deal with several theoretical problems on modern algebra such as units in Group Rings and theory of Ringel-Hall Algebras, using original approaches based on Representation Theory. We are also interested in the applications of these theoretical results in other fields and in their possible algorithmic implementations. Our main directions of research will be: study and computation of primitive central idempotents in group algebras and of primitive idempotents in simple components of group algebras, describing finite sets of generators for a subgroup of finite index in the group of units of an integral group ring, find independent sets of central units of integral group rings, identifying the Gabriel-Roiter inclusions in tame cases and obtaining formulas for the corresponding Ringel-Hall numbers, obtaining formulas for the Ringel-Hall numbers in tame cases, develop and use algorithms related to the topics of the project.


Objectives

 2010
1. Computation of idempotents in group algebras
2011
1. Finding generators for subgroups of finite index in the unit group U(ZG)
2. Identifying the Gabriel-Roiter inclusions in the tame case
3. Develop of GAP algorithms
2012
1. Description of sets of independent central units in the integral group ring ZG and study of possible applications to the Isomorphism Problem
 2. Identifying Gabriel-Roiter inclusions in tame cases and obtaining formulas for the corresponding Ringel-Hall numbers
3. Develop of some GAP algorithms
2013
1. Obtaining formulas for the Ringel-Hall numbers in the tame case
Results
Articles in ISI journals: 9
Articles in IDB journals: 3
Preprints: 4


Articles in ISI journals
  1. I. van Gelder, G. Olteanu, Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents, Finite Fields Appl. 17 (2011), no. 2, 157-165.  pdf
  2. E. Jespers, G. Olteanu, A. del Rio, Rational group algebras of finite groups: from idempotents to units of integral group rings, Algebr. Represent. Theor. 15 (2012), no. 2, 359--377.  http://arxiv.org/abs/1001.1236
  3. Cs. Szanto, I. Szollosi, On preprojective short exact sequences in the Kronecker case, J. Pure Appl. Algebra 216 (2012), No. 5, 1171-1177. pdf
  4. Cs. Szanto, On some Ringel-Hall products in tame cases, J. Pure Appl. Algebra 216 (2012), 2069-2078.
  5. S. Crivei, M.T. Kosan, H. Inankil, G. Olteanu, Correspondences for coclosed submodules, Comm. Algebra 41 (2013), 3635-3647. http://arxiv.org/abs/1203.0729
  6. E. Jespers, G. Olteanu, A. del Rio, I. Van Gelder, Central units of integral group rings, to appear in Proc. Amer. Math. Soc. (2013). http://arxiv.org/abs/1203.5232 (http://www.ams.org/cgi-bin/mstrack/accepted_papers?jrnl=proc)
  7. E. Jespers, G. Olteanu, A. del Rio, I. Van Gelder, Group rings of finite strongly monomial groups: central units and primitive idempotents, J. Algebra 387 (2013), 99--116. http://arxiv.org/abs/1209.1269
  8. I. Szollosi, Computing the extensions of preinjective and preprojective Kronecker modules, J. Algebra, accepted. pdf
  9. G. Olteanu, Baer-Galois connections and applications, Carpathian J. Math., accepted. pdf
Articles in IDB journals
  1. Cs. Szanto, On some nonzero Ringel-Hall numbers in tame cases, Mathematica, Tome 53 (76), No. 2, 2011. pdf
  2. G. Olteanu, Idempotents in group algebras, Mathematica, 54 (77) (2012), 181-194. pdf
  3. I. Szollosi, The extension monoid product of preinjective and preprojective Kronecker modules, Acta Sci. Math., accepted. pdf
Preprints
  1. G. Olteanu, I. Van Gelder, Construction of minimal non-abelian left group codes, submitted. (http://arxiv.org/abs/1302.3747)
  2. Cs. Szanto, On some Ringel-Hall numbers in tame cases, submitted.
  3. Cs. Szanto, I. Szollosi, Ringel-Hall numbers and the Gabriel-Roiter submodules of simple homogeneous modules. (http://arxiv.org/abs/1309.5006)
  4. Cs. Szanto, I. Szollosi, Preinjective subfactors of preinjective Kronecker modules, trimis spre publicare. (http://arxiv.org/abs/1309.4710)
Computer packages
Development of GAP algorithms related to the topics of the project has been achieved. The package Wedderga has been upgrated recently with new functions.
Activities
Reports
Contact data
Address:
Gabriela Olteanu
Faculty of Economics and Business Adminitration
Babes-Bolyai University, Str. T. Mihali 58-60
400591 Cluj-Napoca, Romania
E-mail: gabriela.olteanu at econ dot ubbcluj dot ro
Tel: ++40-264-418652 int.5810
Fax: ++40-264-412570