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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
P001  Natural sciences and mathematics  Mathematics 

Code Science Field
1.01  Natural Sciences  Mathematics 
Keywords
Noncommutative algebra, nonassociative algebra, functional analysis, operator theory, functional identities, preserver problems, adjacency, noncommutative polynomials, elementary operators.
Evaluation (rules)
source: COBISS
Researchers (23)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  19551  PhD Dominik Benkovič  Mathematics  Researcher  2015 - 2021  212 
2.  08721  PhD Matej Brešar  Mathematics  Head  2015 - 2021  829 
3.  18750  PhD Gregor Dolinar  Mathematics  Researcher  2015 - 2021  216 
4.  19550  PhD Daniel Eremita  Mathematics  Researcher  2015 - 2021  134 
5.  20272  PhD Maja Fošner  Administrative and organisational sciences  Researcher  2015 - 2021  218 
6.  29707  PhD Mateja Grašič  Mathematics  Researcher  2017 - 2021  39 
7.  38222  PhD Barbara Ikica  Mathematics  Junior researcher  2015 - 2019 
8.  35334  PhD Urban Jezernik  Mathematics  Junior researcher  2015  33 
9.  23467  PhD Marjetka Knez  Mathematics  Researcher  2015 - 2021  193 
10.  30109  PhD Ganna Kudryavtseva  Mathematics  Researcher  2015 - 2021  132 
11.  01470  PhD Bojan Magajna  Mathematics  Researcher  2015 - 2021  231 
12.  23340  PhD Janko Marovt  Mathematics  Researcher  2015 - 2021  255 
13.  17809  PhD Matej Mencinger  Mathematics  Researcher  2015 - 2021  214 
14.  07680  PhD Tatjana Petek  Mathematics  Researcher  2015 - 2021  129 
15.  33288  PhD Lucijan Plevnik  Mathematics  Researcher  2016 - 2021  24 
16.  51878  PhD Gregor Podlogar  Mathematics  Junior researcher  2018 - 2021 
17.  17808  PhD Rok Strašek  Mathematics  Researcher  2015 - 2021  142 
18.  13431  PhD Sašo Strle  Mathematics  Researcher  2015 - 2021  116 
19.  05953  PhD Peter Šemrl  Mathematics  Researcher  2015 - 2021  497 
20.  33617  PhD Špela Špenko  Mathematics  Researcher  2015 - 2016  36 
21.  54105  Tea Štrekelj  Mathematics  Junior researcher  2020 - 2021 
22.  36360  PhD Aljaž Zalar  Mathematics  Researcher  2015 - 2021  55 
23.  19886  PhD Emil Žagar  Mathematics  Researcher  2015 - 2021  187 
Organisations (2)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,257 
2.  2547  University of Maribor, Faculty of natural sciences and mathematics  Maribor  5089638051  18,074 
Abstract
The members of the programme team deal with various mathematical areas. The emphasis, however, is on noncommutative algebra and its applications to other fields, particularly to functional analysis. Among the more important research topics of the core of the group we can point out functional identities, the study of nonassociative structures in associative algebras, linear and nonlinear preservers, the study of evaluations of noncommutative polynomials on matrices, and elementary operators, derivations, and automorphisms on operator and other algebras. Among several topics that will be considered, we point out two. One of our important goals is to continue the development of the theory of functional identities. Roughly speaking, the existing theory gives definitive answers for infinite dimensional prime algebras. We intend to extend the theory to finite dimensional algebras, where the results are expected to be considerably more complicated. Also, it is our aim to consider functional identities on some algebras containing nonzero nilpotent ideals (e.g., in triangular algebras). One of the constant goals is to find new applications of functional identities in other mathematical areas, especially in Lie theory.   The second important goal is to continue and possibly complete the work on optimal versions of Hua's fundamental theorems of geometry of matrices. These theorems describe the general form of bijective maps on various matrix spaces that preserve adjacency in both directions. The ultimate goal is to describe such maps under weaker assumptions (without bijectivity assumption, preserving adjacency in one direction only, maps between matrix spaces of different sizes) and give examples showing the optimality of the obtained results. We will find new applications to the theory of preservers, mathematical physics, and geometry.
Significance for science
The number of citations of papers by group members, invited lectures at conferences, and memberships in editorial boards give evidence of the importance of the programme for the development of science.
Significance for the country
The research programme is devoted to basic research. Therefore we do not expect that the results of the programme will have a direct impact on the economic development of Slovenia. On the other hand, the programme is  very important for the development of (especially graduate) university programmes. It is also of importance for Slovenian science in order to keep it at an internationally recognized level. The programme team is formed from mathematicians from two universities, i.e., University of Ljubljana and University of Maribor. Keeping a fruitful  cooperation between researchers from these two centers is one of the goals of the programme.
Most important scientific results Annual report 2015, interim report
Most important socioeconomically and culturally relevant results Annual report 2015, interim report
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