Q:

Question about Lie superalgebra.

What are the generators and relations for the Lie superalgebra $\mathfrak{psu}(2, 2 | 4)$? Thank you very much.

A:

The article arXiv:0505234, "Non-linear Realization of $\operatorname{PSU}(2,2|4)$ on the Light-Cone" by Pierre Ramond et al. has details and further references.
The algebra has 30 bosonic generators forming direct product of conformal algebra $\mathfrak{su}(2,2) \sim \mathfrak{so}(4,2)$ (15 generators) and internal $\mathfrak{su}(4) \sim \mathfrak{so}(6)$ (also 15 generators), as well as 32 fermionic generators. 
Fermionic generators form a representation of $\mathfrak{su}(2,2) \otimes \mathfrak{su}(4)$ under adjoint action of bosonic sub-algebra.

