Lower bounds for algebraic complexity of classical simple Lie algebras

Exact algebraic algorithms for classical simple Lie algebras over fields of characteristic zero are considered. The complexity of an algebra in this computational model is defined as the number of (non-scalar) multiplications of an optimal algorithm (calculating the product of two elements of the algebra). Lower bounds for the algebraic complexity are obtained for algebras in the series $A_l$, $B_l$, $C_l$ and $D_l$.
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