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arXiv · 2309.16199

Primitive elements of a connected free bialgebra

Loïc Foissy
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Abstract

We prove that the Lie algebra of primitive elements of a graded and connected bialgebra, free as an associative algebra, over a eld of characteristic zero, is a free Lie algebra. The main tool is a ltration, which allows to embed the associated graded Lie algebra into the Lie algebra of a free and cocommutative bialgebra. The result is then a consequence of Cartier-Quillen-Milnor-Moore's Shirshov-Witt's theorems.

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Loïc Foissy. 2023-09-28. Primitive elements of a connected free bialgebra. https://arxiv.org/abs/2309.16199

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