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

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