We prove the equivalence of two presentations of deformed double current
algebras associated to a complex simple Lie algebra, the first one obtained via
a degeneration of affine Yangians while the other one naturally appeared in the
construction of the elliptic Casimir connection. We also construct a specific
central element of these algebras and, in type A, show that they contain a very
large center for certain values of their parameters.Comment: 40 page