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

2024/01/12 by Schmitz, Leonard, Tapia, Nikolas
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2401.06691

Abstract

Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from B_∞-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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