Theory of Lie algebras and groups, theory of classical and quantum integrable systems.
Main publications:
T. Skrypnyk, “Quasigraded Lie algebras, the Kostant-Adler scheme, and integrable hierarchies”, Theoret. and Math. Phys., 142:2 (2005), 275–288
T. Skrypnyk, “Quantum integrable systems, non-skew-symmetric $r$-matrices and algebraic Bethe ansatz”, J. Math. Phys., 48:2 (2007), 023506, 14 pp.
T. Skrypnyk, “Integrable quantum spin chains, non-skew symmetric $r$-matrices and quasigraded Lie algebras.”, J. Geom. Phys., 57:1 (2006), 53–67
T. Skrypnyk, “Generalized $n$-level Jaynes–Cummings and Dicke models, classical rational $r$-matrices and algebraic Bethe ansatz”, J. Phys. A, 41:47 (2008), 475202, 21 pp.
T. Skrypnyk, “Isomonodromic deformations, generalized Knizhnik–Zamolodchikov equations and non-skew-symmetric classical $r$-matrices”, J. Math. Phys., 2010:8
papernumber 083516 (51), 24 pp.
