  We study the $TT$ OPE in $d>2$ CFTs whose bulk dual is Einstein gravity.
Directly from the $TT$ OPE, we obtain, in a certain null-like limit, an
algebraic structure consistent with the Jacobi identity: $[{\cal L}_m, {\cal
L}_n]= (m-n) {\cal L}_{m+n}+ C m (m^2-1) \delta_{m+n,0}$. The dimensionless
constant $C$ is proportional to the central charge $C_T$. Transverse integrals
in the definition of ${\cal L}_m$ play a crucial role. We comment on the
corresponding limiting procedure and point out a curiosity related to the
central term. A connection between the $d>2$ near-lightcone stress-tensor
conformal block and the $d=2$ $\cal W$-algebra is observed. This note is
motivated by the search for a field-theoretic derivation of $d>2$ correlators
in strong coupling critical phenomena.
