Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras
are described. It is proven that all principal Galilean Lie algebras do not have non-trivial 1 2 …

It is demonstrated that the Pais–Uhlenbeck oscillator in arbitrary dimension enjoys the l-
conformal Newton–Hooke symmetry provided frequencies of oscillation form the arithmetic …

We show that the Inönü-Wigner contraction of so (ℓ+ 1, ℓ+ d) with the integer ℓ> 1 may lead
to algebra which contains a variety of conformal extensions of the Galilei algebra as …

We discuss a procedure to determine finite sets M within the commutant of an algebraic
Hamiltonian in the enveloping algebra of a Lie algebra g such that their generators define a …

Dynamical systems invariant under the action of the l-conformal Newton–Hooke algebras
are constructed by the method of nonlinear realizations. The relevant first order Lagrangians …

The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et
al.(2014)[24] is continued with special emphasis put on the Hamiltonian formalism. The …

In two recent papers (Aizawa et al., 2013 [15]) and (Aizawa et al., 2015 [16]), representation
theory of the centrally extended l-conformal Galilei algebra with half-integer l has been …

In recent years nonrelativistic (super) conformal algebras have attracted considerable
attention. 1–35 On the one hand, this interest originates from the current investigation of the …

We introduce a search algorithm that utilises differential operator realisations to find
polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two …

We investigate the real Lie algebra of first-order differential operators with polynomial
coefficients, which is subject to the following requirements.(1) The Lie algebra should admit …