Bracket width of current Lie algebras

The length of an element z of a Lie algebra L is defined as the smallest number s needed to represent z as a sum of s brackets. The bracket width of L is defined as supremum of the lengths of its elements. Given a finite-dimensional simple Lie algebra g over an algebraically closed field k of characteristic zero, we study the bracket width of current Lie algebras L= g⊗ A. We show that for an arbitrary A the width is at most 2. For $A=k[[t]]$ and $A=k[t]$ we compute the width for algebras of types A and C.