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arXiv · 2401.06691

Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra

Leonard Schmitz·Nikolas Tapia
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Abstract

Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from $\mathbf{B}_\infty$-algebras and a novel two-parameter Hoffman exponential, we provide three classes of isomorphisms between the underlying two-parameter shuffle and quasi-shuffle algebras. In particular, we provide a Hopf algebraic connection to the (classical, one-parameter) shuffle algebra over the extended alphabet of connected matrix compositions.

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Leonard Schmitz, Nikolas Tapia. 2024-01-12. Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra. https://arxiv.org/abs/2401.06691

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