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arXiv · 1705.08132

Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group

Loïc Foissy
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Abstract

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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Loïc Foissy. 2017-05-23. Extension of the product of a post-Lie algebra and application to the SISO feedback transformation group. https://arxiv.org/abs/1705.08132

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