Projects / Programmes
January 1, 2015
- December 31, 2021
| 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 |
Noncommutative algebra, nonassociative algebra, functional analysis, operator theory, functional identities, preserver problems, adjacency, noncommutative polynomials, elementary operators.
Researchers (23)
Organisations (2)
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
