Non-uniqueness of the natural and projectively equivariant quantization

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In [3], the authors showed the existence and the uniqueness of a sl(m+1,)-equivariant quantization in the non-critical situations. The curved generalization of the sl(m+1,)-equivariant quantization is the natural and projectively equivariant quantization. In [1] and [7], the existence of such a quantization was proved in two different ways. In this paper, we show that this quantization is not unique.