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Hopf algebras, from basics to applications to renormalization

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arxiv math/0408405 v2 pith:73WGXS5J submitted 2004-08-30 math.QA hep-thmath.CO

Dominique Manchon This is my paper · ORCID
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keywords algebrashopfrenormalizationapplicationsaspectsbasicsbirkhoffbogota
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An extended version of a series of lectures given at Bogota in december 2002. It consists in a presentation of some aspects of Connes' and Kreimer's work on renormalization in the context of general connected Hopf algebras, in particular Birkhoff decomposition and, in the graded case, the scattering-type formula.

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Cited by 2 Pith papers

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    math.RT 2026-07 accept novelty 7.0 of 10

    Every k-tensor is the unique sum of an m-piecewise-symmetric tensor and a (k-m)-piecewise-alternating tensor; the latter space is the annihilator of level-k signatures of m-segment paths.

  2. Explicit and Effectively Symmetric Schemes for Neural SDEs on Lie Groups

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    Introduces the first explicit near-reversible integrator for neural SDEs on Lie groups by extending EES schemes with Bazavov's commutator-free lift, achieving better stability and up to 10x memory reduction on manifol...

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