Research team

Assoc.
Prof. Dr. Gabriela
Olteanu (project manager)

Assoc. Prof. Dr. Csaba Szanto

Teaching assist. Dr. Stefan Suteu Szollosi

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 2. Identifying the Gabriel-Roiter inclusions in the tame case

3. Develop of GAP algorithms

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

20132. Identifying Gabriel-Roiter inclusions in tame cases and obtaining formulas for the corresponding Ringel-Hall numbers

3. Develop of some GAP algorithms

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 IDB journals: 3

Preprints: 4

Articles in ISI journals

- 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
- 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

- Cs. Szanto, I. Szollosi, On preprojective short exact sequences in the Kronecker case, J. Pure Appl. Algebra 216 (2012), No. 5, 1171-1177. pdf
- Cs. Szanto, On some Ringel-Hall products in tame cases, J. Pure Appl. Algebra 216 (2012), 2069-2078.
- 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
- 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)
- 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
- I. Szollosi, Computing the extensions of preinjective and preprojective Kronecker modules, J. Algebra, accepted. pdf

- G. Olteanu, Baer-Galois connections and applications, Carpathian J. Math., accepted. pdf

- Cs. Szanto, On some nonzero Ringel-Hall numbers in tame cases, Mathematica, Tome 53 (76), No. 2, 2011. pdf
- G. Olteanu, Idempotents in group algebras, Mathematica, 54 (77) (2012), 181-194. pdf
- I. Szollosi, The extension monoid product of preinjective and preprojective Kronecker modules, Acta Sci. Math., accepted. pdf

- G. Olteanu, I. Van Gelder, Construction of minimal non-abelian left group codes, submitted. (http://arxiv.org/abs/1302.3747)
- Cs. Szanto, On some Ringel-Hall numbers in tame cases, submitted.
- Cs. Szanto, I. Szollosi, Ringel-Hall numbers and the Gabriel-Roiter submodules of simple homogeneous modules. (http://arxiv.org/abs/1309.5006)

- Cs. Szanto, I. Szollosi, Preinjective subfactors of preinjective Kronecker modules, trimis spre publicare. (http://arxiv.org/abs/1309.4710)

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

- Research visit: Gabriela Olteanu,
September 9-19, 2010, Vrije Universiteit Brussel, Belgium, to prof. Eric
Jespers.

- Research visit: Csaba Szanto,
November 15-21, 2010, Budapest, Hungary.

- Research visit: Stefan Suteu Szollosi, October 2-14, 2010, St. Andrews, Great Britain, prof. Alexander Konovalov. Talk given at the department seminar with the title: On the Ringel-Hall product of preinjective Kronecker modules and the matrix subpencil problem
- Conference attendance: Gabriela Olteanu, Quantitative Methods in Economics, Babes-Bolyai University, Cluj-Napoca, November 12-13, 2010. Talk with the title: Decompositions of semisimple group algebras.
- Conference attendance: Gabriela Olteanu, The Seventh Congress of Romanian Mathematicians, Brasov, Romania, June 29–July 5, 2011. Talk with the title: Idempotents in rational group algebras.
- Conference attendence: Stefan Suteu Szollosi, New developments in noncommutative algebra and its applications (Workshop), Sabhal Mòr Ostaig, Isle of Skye, Scotland, June 26 - July 2, 2011. Poster with the title: Short exact sequences of Kronecker modules.
- Research visit: Gabriela Olteanu, July 15-August 1, 2011, University of Murcia, Spain, to prof. Angel del Rio.
- Conference attendance: Stefan Suteu Szollosi, Groups and Semigroups: Interactions and Computations (Conference), University of Lisbon, Portugal, July 25-29, 2011. Talk with the title: Computing the extensions of preinjective and preprojective Kronecker modules.
- Conference attendance: Stefan Suteu Szollosi, Algebraic Representation Theory, Uppsala University, Sweden, September 1-3, 2011. Talk with the title: On short exact sequences of Kronecker module.
- Conference attendance: Gabriela Olteanu, Some Trends in Algebra, Prague, Czech Republic, September 6–10, 2011. Talk with the title: Idempotents in rational group algebras.
- Research visit: Csaba Szanto, September 18-27, 2011, ELTE University Budapest, Hungary. Talk given at the Renyi Mathematical Institute at 26th of September 2011 with the title: Embedding Kronecker modules.
- Communications session: Stefan Suteu Szollosi, Sesiune de comunicare ştiinţifică (POS DRU 6/1.5/S/3), Babeş-Bolyai University, Cluj-Napoca, Romania, September 30, 2011. Poster with the title: Short exact sequences of Kronecker modules.
- Department Seminar: Stefan Suteu Szollosi, Babes-Bolyai University, Cluj-Napoca, September 28, 2011. Talk with the title: Kronecker modules and matrix pencils.

- Research visit: Csaba Szanto, November 9-13, 2011, ELTE University Budapest, Hungary.
- Research visit: Gabriela Olteanu, November 16-21, 2011, ELTE University Budapest, Hungary, to prof. I. Agoston.

- Research visit: Stefan Suteu Szollosi, November 18-22, 2011, University Budapest, Hungary, to prof. M. Domokos.
- Thesis public defence: Stefan Suteu Szollosi, December 20, 2011, Babes-Bolyai University, Cluj-Napoca. Title of the Ph.D. thesis: Kronecker modules and matrix pencils.
- Research visit: Gabriela Olteanu, April 18-28, 2012, Vrije Universiteit Brussel, Belgium, to prof. Eric Jespers.
- Research visit: Csaba Szanto, May 20-27, 2012, University Budapest, Hungary, to prof. I. Agoston. Talk given at the Renyi Mathematical Institute with the title: The Gabriel-Roiter measure and the Ringel-Hall polynomials.
- Research visit: Stefan Suteu Szollosi, May 23-27, 2012, Eotvos Lorand University Budapest, Hungary, to prof. Istvan Agoston. Talk with the title: Kronecker modules and the matrix subpencil problem.
- Conference attendance: Stefan Suteu Szollosi, Young Algebraists' Conference 2012, Ecole Polytechnique Federale de Lausanne, Switzerland, June 11-15 2012.
- Conference attendance: Gabriela Olteanu, Workshop "Group Rings ans related topics", University of Stuttgart, Germany, June 25-29, 2012. Talk with the title: Idempotents in group algebras.
- Conference attendance: Stefan Suteu Szollosi, CSM-The Second Conference of PhD Sudents in Mathematics, Szeged, Hungary, June 28-30, 2012. Talk with
the title:
*On short exact sequences of Kronecker modules.* - Conference attendance: Stefan Suteu Szollosi, Workshop and International Conference on Representations of Algebras (ICRA 2012), University of Bielefeld, August 8-17, 2012.
- Conference attendance: Csaba Szanto, International Conference on Representations of Algebras (ICRA 2012), University of Bielefeld, August 13-17, 2012. Talk with
the title: On Ringel-Hall products and extensions in tame cases.

- Conference attendance: Gabriela Olteanu, International Conference on Representations of Algebras (ICRA 2012), University of Bielefeld, August 13-17, 2012. Talk with the title: Constructing idempotents in group algebras.
- Conference attendance: Stefan Suteu Szollosi, open Suse Conference, Czech Technical University, Prague, Chech Republic, October 20-23, 2012.
- Research visit: Csaba Szanto, November 9-12, 2012, University Budapest, Hungary, to prof. I. Agoston.
- Conference attendance: Gabriela Olteanu, Algebra Symposium, Cluj-Napoca, April 19-20, 2013. Talk with the title: Construction of group codes.
- Conference attendance: Stefan Suteu Szollosi, Algebra Symposium, Cluj-Napoca, April 19-20, 2013. Talk with the title: On the extension monoid product of Kronecker modules.
- Research visit: Csaba Szanto, April 14-21, 2013,
ELTE University Budapest, Hungary, to prof. I. Agoston. Talk
given at the Renyi Mathematical Institute at 15th of April 2013 with the
title:
*On Gabriel-Roiter exact sequences.* - Conference attendance: Gabriela Olteanu, Rings, Categories and Hopf Algebras, May 18-19, 2013, Bucharest. Talk with the title: Primitive idempotents in semisimple group algebras.
- Conference attendance: Csaba Szanto, Rings, Categories and Hopf Algebras, May 18-19, 2013, Bucharest. Talk with the title: Extensions and Ringel-Hall algebras in tame cases.
- Conference attendance: Stefan Suteu Szolosi, Rings, Categories and Hopf Algebras, May 18-19, 2013, Bucharest. Talk with the title: The matrix subpencil problem via Kronecker modules.

- Conference attendance: Gabriela Olteanu, Recent Trends in Rings and Algebras, June 3-7, 2013, Murcia, Spain. Talk with the title: Construction of minimal non-abelian left group codes.
- Conference attendance: Gabriela Olteanu, Joint International Meeting of the AMS and the Romanian Mathematical Society, June 27-30, 2013, Alba Iulia, Romania. Poster with the title: Semisimple group algebras: primitive idempotents and minimal left group codes.
- Research visit: Gabriela Olteanu, September 7-17, 2013, University of Murcia, Spain, to prof. Angel del Rio.
- Conference attendance: Gabriela Olteanu, 9-th International Conference on Applied Mathematics (ICAM9), September 25-28, 2013, Baia-Mare, Romania. Talk with the title: Semisimple group algebras: primitive idempotents and group codes.

- Conference attendance: Csaba Szanto, 9-th International Conference on Applied Mathematics (ICAM9), September 25-28, 2013, Baia-Mare, Romania. Talk with the title: Extensions of modules over tame hereditary algebras
- Conference attendance: Stefan Suteu Szolosi, 9-th International Conference on Applied Mathematics (ICAM9), September 25-28, 2013, Baia-Mare, Romania.
- Research visit: Csaba Szanto, October 12-27, 2013, University of Stuttgart, Germany, to prof. S. Koenig. Talk with the title: Ringel-Hall polynomials and Gabriel-Roiter measure over Euclidean quivers.
- Research visit: Stefan Suteu Szolosi, October 12-27, 2013, University of Stuttgart, Germany, to prof. S. Koenig. Talk with the title: Combinatorics of Kronecker modules with applications to the matrix subpencil problem.

Reports

Contact data

Address:

Tel: ++40-264-418652 int.5810

Fax: ++40-264-412570

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 roFaculty of Economics and Business Adminitration

Babes-Bolyai University, Str. T. Mihali 58-60

400591 Cluj-Napoca, Romania

Tel: ++40-264-418652 int.5810

Fax: ++40-264-412570