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Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group
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We describe the both post-and pre-Lie algebra g SISO associated to the affine SISO feedback transformation group. We show that it is a member of a family of post-Lie algebras associated to representations of a particular solvable Lie algebra. We first construct the extension of the magmatic product of a post-Lie algebra to its enveloping algebra, which allows to describe free post-Lie algebras and is widely used to obtain the enveloping of g SISO and its dual.
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On post-Lie structures for free Lie algebras
For graded post-Lie structures on free Lie algebras, the coproduct dual to the Grossman-Larson product is given explicitly, yielding new dual Hopf algebra descriptions for the Ihara and ari brackets and a conjectural ...
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