Related papers: Lie-algebraic structure of 2D harmonic oscillator …

We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies…

This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.

There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting…

In this paper we construct the coherent and trajectory-coherent states of a damped harmonic oscillator. We investigate the properties of this states.

We propose a new definition of so called Hamiltonian forms in n-plectic geometry and show that they have a non-trivial Lie infinity-algebra structure.

We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that…

In this paper, we investigate the integrability aspects of a physically important nonlinear oscillator which lacks sufficient number of Lie point symmetries but can be integrated by quadrature. We explore the hidden symmetry, construct a…

A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the…

We investigate Lie algebras endowed with a complex symplectic structure and develop a method, called \emph{complex symplectic oxidation}, to construct certain complex symplectic Lie algebras of dimension $4n+4$ from those of dimension $4n$.…

The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method,…

We present two constructions of complex symplectic structures on Lie algebras with large abelian ideals. In particular, we completely classify complex symplectic structures on almost abelian Lie algebras. By considering compact quotients of…

We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.

In this work we study the existence of invariant almost complex structures on real flag manifolds associated to split real forms of complex simple Lie algebras. We show that, contrary to the complex case where the invariant almost complex…

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.

Hom-Lie algebras defined on central extensions of a given quadratic Lie algebra that in turn admit an invariant metric, are studied. It is shown how some of these algebras are naturally equipped with other symmetric, bilinear forms that…

On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-K\"ahler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

The classification of graded non-alternating Hamiltonian Lie algebras over perfect field of characteristic 2 is obtained. It is shown that the filtered deformations of such algebras correspond to non-alternating Hamiltonian forms with…

We construct the universal enveloping algebra of a Hom-Lie algebra and endow it with a Hom-Hopf algebra structure. We discuss group-like elements that we see as a Hom-group integrating the initial Hom-Lie algebra.