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An operad is never free as a pre-Lie algebra

Published 7 Feb 2017 in math.RA | (1702.01949v1)

Abstract: An operad is naturally endowed with a pre-Lie structure. We prove that as a pre-Lie algebra an operad is not free. The proof holds on defining a non-vanishing linear operation in the pre-Lie algebra which is zero in any operad.

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