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Projects / Programmes source: ARIS

Algebras and rings

Periods
Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

Code Science Field
P120  Natural sciences and mathematics  Number theory, field theory, algebraic geometry, algebra, group theory 

Code Science Field
1.01  Natural Sciences  Mathematics 
Keywords
algebra, ring, Banach algebra, operator algebra, Lie algebra, Jordan algebra, operator, functional identities, linear preservers, derivation, automorphism.
Evaluation (rules)
source: COBISS
Researchers (25)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  19551  PhD Dominik Benkovič  Mathematics  Researcher  2009 - 2014  211 
2.  08721  PhD Matej Brešar  Mathematics  Head  2009 - 2014  828 
3.  18750  PhD Gregor Dolinar  Mathematics  Researcher  2009 - 2014  214 
4.  19550  PhD Daniel Eremita  Mathematics  Researcher  2009 - 2014  133 
5.  20272  PhD Maja Fošner  Administrative and organisational sciences  Researcher  2009 - 2014  217 
6.  06084  PhD Bojan Hvala  Mathematics  Researcher  2009 - 2014  244 
7.  35334  PhD Urban Jezernik  Mathematics  Junior researcher  2012 - 2014  32 
8.  23467  PhD Marjetka Knez  Mathematics  Researcher  2013 - 2014  193 
9.  19549  PhD Irena Kosi Ulbl  Mathematics  Researcher  2009 - 2013  103 
10.  30109  PhD Ganna Kudryavtseva  Mathematics  Researcher  2012 - 2014  131 
11.  02297  PhD Peter Legiša  Mathematics  Researcher  2009 - 2014  455 
12.  07082  PhD Gorazd Lešnjak  Mathematics  Researcher  2009 - 2014  154 
13.  01470  PhD Bojan Magajna  Mathematics  Researcher  2009 - 2014  231 
14.  23340  PhD Janko Marovt  Mathematics  Researcher  2010 - 2014  255 
15.  17809  PhD Matej Mencinger  Mathematics  Researcher  2009 - 2014  210 
16.  07680  PhD Tatjana Petek  Mathematics  Researcher  2009 - 2014  129 
17.  33288  PhD Lucijan Plevnik  Mathematics  Junior researcher  2010 - 2014  24 
18.  32024  PhD Tina Rudolf  Mathematics  Junior researcher  2009 - 2014 
19.  17808  PhD Rok Strašek  Mathematics  Researcher  2009 - 2014  142 
20.  05953  PhD Peter Šemrl  Mathematics  Researcher  2009 - 2014  496 
21.  33617  PhD Špela Špenko  Mathematics  Junior researcher  2011 - 2014  36 
22.  04310  PhD Joso Vukman  Mathematics  Researcher  2009 - 2014  325 
23.  36360  PhD Aljaž Zalar  Mathematics  Junior researcher  2013 - 2014  54 
24.  11719  PhD Borut Zalar  Mathematics  Researcher  2009 - 2014  317 
25.  19886  PhD Emil Žagar  Mathematics  Researcher  2013 - 2014  186 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,643 
Abstract
The major part of this research program is devoted to the study of mappings on rings and algebras. The methods that are used are primarily algebraic ones, though many of our results are functional analytic and operator theoretic. Namely, algebraic methods that we have developed in the past have proved to be useful in the analytic setting. One of our main goals is to continue the study of functional identities. Roughly speaking, a functional identity can be described as an identical relation holding for all elements from a ring (algebra) that involves arbitrary (unknown) functions. The goal is to describe the form of these functions. Sometimes this is not possible, but in that case one can characterize the structure of the ring (algebra); often these exceptional cases occur in low dimensional algebras. It seems that the general theory of functional identities is close to its completion. One of our goals is to give a significant contribution to this project in which several mathematicians from different countries are involved. The results on functional identities have turned out to be applicable to several mathematical areas, for example to the theory of Lie algebras (Lie isomorphisms, Lie derivations, Lie-admissible algebras), the theory of Jordan algebras (Jordan mappings), the theory of (generalized) polynomial identities, linear preserver problems (commutativity preservers, normal preservers), automatic continuity theory, mathematical physics, etc. It seems reasonable to conjecture that there are still many possibilities for further applications, and this is one of our main goals. In this context some functional identities appear that are not covered by the general theory. The treatment of such special identities is also one of our intentions. The theory of derivations and automorphisms (and related mappings) is a classical area in both algebra and functional analysis. Some important old problems are still open (for example, the noncommutative Singer-Wermer conjecture). We intend to continue working in this area. A special challenge for us is to find applications of algebraic methods in solving analytic problems.
Significance for science
A large number of citations and other responses on the work of the members of the program show that the program is important for the development of science.
Significance for the country
The research work within the research program is in the area of pure mathematics, therefore the results of the research do not have a direct impact on the economical development of Slovenia. However, the program is very important for the development of the university curriculums (especially postgraduate ones). It also enables scientist from Slovenia to work on the most up to date research problems at the same time as researchers from all over the world.
Audiovisual sources (1)
no. Title (with video link) Event Source
1. Algebras and rings    Research programme video presentation 
Most important scientific results Annual report 2009, 2010, 2011, 2012, 2013, final report, complete report on dLib.si
Most important socioeconomically and culturally relevant results Annual report 2009, 2010, 2011, 2012, 2013, final report, complete report on dLib.si
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