Towards $\ell$-conformal Galilei algebra via contraction of the conformal group

Abstract

We show that the In\"{o}n\"{u}-Wigner contraction of $so(\ell+1,\ell+d)$ with the integer $\ell>1$ may lead to algebra which contains a variety of conformal extensions of the Galilei algebra as subalgebras. These extensions involve the $\ell$-conformal Galilei algebra in $d$ spatial dimensions as well as $l$-conformal Galilei algebras in one spatial dimension with $l=3$, $5$, ..., $(2\ell-1)$.