Journal of Integer Sequences, Vol. 23 (2020), Article 20.2.5

The Lie Bracket and the Arithmetic Derivative

Jun Fan and Sergey Utev
Department of Mathematics
University of Leicester
Leicester LE1 7RH
United Kingdom


We apply the Lie bracket approach to characterize the semi-derivations on the positive integers. The approach is motivated by the Stroock-Lie bracket identity commonly used in Malliavin calculus.

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Received July 26 2019; revised version received February 19 2020. Published in Journal of Integer Sequences, February 19 2020.

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