  The even spin W^e_\infty algebra that is generated by the stress energy
tensor together with one Virasoro primary field for every even spin s \geq 4 is
analysed systematically by studying the constraints coming from the Jacobi
identities. It is found that the algebra is characterised, in addition to the
central charge, by one free parameter that can be identified with the
self-coupling constant of the spin 4 field. We show that W^e_\infty can be
thought of as the quantisation of the asymptotic symmetry algebra of the even
higher spin theory on AdS_3. On the other hand, W^e_\infty is also quantum
equivalent to the so(N) coset algebras, and thus our result establishes an
important aspect of the even spin minimal model holography conjecture. The
quantum equivalence holds actually at finite central charge, and hence opens
the way towards understanding the duality beyond the leading 't Hooft limit.
