Saša Krešić-Jurić, noncommutative spaces, integrable systems
Tea Martinic-Bilac, noncommutative spaces
The research is focused on realizations of noncommutative spaces in the context of deformation theory and their applications to geometry and physics. Specifically, we investigate realizations of the kappa-deformed space, the Lorentz and Poincare algebras as well as general Lie-algebra type noncommutative spaces by formal power series in the Heisenberg-Weyl algebras and their generalizations. We also study realizations of some Lie superalgebras which arise naturally in the geometry of differential forms on noncommutative spaces. A part of the research is devoted to investigation of Lie algebraic methods in integrable systems, in particular application of the Riemann-Hilbert problem on loop groups in studying integrability and symmetries of some nonlinear evolution equations. In the near future we plan to study integrable discretizations and geometric numerical integration of evolution equations which can be formulated as a Lax pair or zero-curvature equation with a spectral parameter.
Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions (with S. Meljanac and T. Martinic-Bilac) J. Math. Phys. 61, 051705 (2020).
Generalization of Weyl realization to a class of Lie superalgebras (with S. Meljanac and D. Pikutic), J. Math. Phys. 59 (2), 021701 (2018).
Realization of bicovariant differential calculus on Lie algebra type noncommutative spaces (with S. Meljanac and T. Martinic), J. Math. Phys. 58, 071701 (2017).
The Weyl realization of Lie algebras and left-right duality (with S. Meljanac and T. Martinic), J. Math. Phys. 57, 051704 (2016).
Differential algebras on kappa-Minkowski space, and kappa-Poincare algebra (with S. Meljanac), Int. J. Mod. Phys. A 26 (20), 3385-3402 (2011).