Serre type relations for special linear Lie superalgebras

It is pounted out that, for m,n ≥ 2, the naive Serre presentation corresponding to the simplest Cartan matrix of sl(m,n) does not define the Lie superalgebra sl(m,n) but a larger algebra s(m,n) of which sl(m,n) is a non-trivial quotient. The supplementary relations for the generators are found and the definition of the q-deformed universal enveloping algebra of sl(m,n) is modified accordingly. (orig.)