We give a review of some group-theoretical results related to nonrelativistic holography. Our
main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall …

We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial
dimension. We construct a functor which transforms simple modules with nonzero central …

The ℓ-conformal Galilei algebra, denoted by ${\mathfrak {g}} _ {\ell}(d), $ is a non-
semisimple Lie algebra specified by a pair of parameters (d, ℓ). The algebra is regarded as a …

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 …

In this paper we use Block's classification of simple modules over the first Weyl algebra to
obtain a complete classification of simple weight modules, in particular, of Harish-Chandra …

Structure of The Planar Galilean Conformal Algebra - ScienceDirect Skip to main contentSkip
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In this paper, we classify simple Whittaker modules and simple quasi-Whittaker modules for
the Euclidean Lie algebra E= e (3). We show that a simple e (3)-module is a Whittaker …

N= 2 supersymmetric extensions of Galilean conformal algebra (GCA), specified by spin l
and dimension of space d, are investigated. Duval and Horváthy showed that the l= 1/2 GCA …

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 …