Invariant metrics on current Lie algebras

In this work we state conditions for a current Lie algebra g⊗S to admit an invariant metric, where g is a quadratic Lie algebra and S is an associative and commutative algebra with unit. We show that if g is an indecomposable quadratic Lie algebra, then g⊗S admits an invariant metric if and only if S also admits an invariant metric. In addition, we prove a theorem similar to the double extension for g⊗S, where g is an indecomposable, nilpotent and quadratic Lie algebra.