Tag Archives: Lie derivatives

Pre-Lie algebras, Cayley’s analytic trees, and mathemagical forests

Referring to week 299 of John Baez’s old blog or the Pre-Lie Algebra entry of nLab, a left pre-Lie algebra satisfies the associative relation, (AR), . To see the relation to Cayley’s work of 1857 as described in my pdf … Continue reading

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A Class of Differential Operators and the Stirling Numbers

The differential operator with can easily be expanded in terms of the operators by considering its action on

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The Bernoulli polynomials and Hirzebruch’s generalized Todd class

Let’s connect the Bernoullis, using their basic operational definition rather than their e.g.f., to the Todd genus and more through formal group laws (FGL, see note at bottom) and associated Lie ops and, therefore, compositional inversion. [This is done through … Continue reading

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Bernoulli, Blissard, and Lie meet Stirling and the simplices: State number operators and normal ordering

A set of identities that encapsulates relations among the Bernoulli numbers, the Stirling numbers of the first and second kinds, and operators related to the umbral calculus of Blissard and his contemporaries: Decoding:

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Goin’ with the Flow: Logarithm of the Derivative

Goin’ with the Flow: Logarithm of the Derivative Operator is a pdf set of notes under construction on the relations between the commutator of the logarithm of the derivative operator, the Pincherle derivative,  Lie operator derivatives, and the two umbrally inverse … Continue reading

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