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

19.04.2024, 11:00 Uhr  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Leonard Schmitz (MPI Leipzig)

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. This is joint work with Nikolas Tapia.

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