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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=kt we compute the width for algebras of types A and C.
Kunyavskiı̆ et al. (Tue,) studied this question.
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