In this paper, Jordan–Kronecker invariants are calculated for all nilpotent 6- and 7-dimensional Lie algebras. We consider the Poisson bracket family, depending on lambda parameter a coalgebra, i.e., linear space dual to algebra. For some

The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2, R) coalgebra symmetry. By using the properties induced by such a coalgebra structure, it can be proven that the introduction of any quantum deformation of the sl(2, R) algebra will provide an integrable deformation for such systems...

The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures meromorphically induced by conformal equivalence classes of worldsheets. We then show this category is isomorphic to the category of vertex operator coalgebras...

Coalgebra is used to generalize notions and techniques from concurrency theory, in order to apply them to problems concerning the supervisory control of discrete event systems. The main ingredients of this approach are the characterization of controllability in terms of (a variant of) the notion of bisimulation, and the observation that the family of (partial) languages carries a final coalgebr...

The recent interest in the study of higher-rank polynomial algebras related to $n$-dimensional classical and quantum superintegrable systems with coalgebra symmetry their connection generalised Racah algebra $R(n)$, a generalisation rank one $R(3)$, raises problem understanding role played by $n - 2$ quadratic subalgebras generated left right Casimir invariants (sometimes referred as universal ...

Motivated by issues in designing practical total functional programming languages, we are interested in structured recursive equations that uniquely describe a function not because of the properties of the coalgebra marshalling the recursive call arguments but thanks to the algebra assembling their results. Dualizing the known notions of recursive and wellfounded coalgebras, we call an algebra ...

A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of nonconstant curvature. Such a curvature depends on the quantum deformation parameter z and the flat case is recovered in the limit z → 0. A superintegrable geodesic dynamics can also be defined in the same framework, and the corresponding spa...