What question did this study set out to answer?

To unify and generalize the existing types of braid and tie algebras in literature, including new variants.

July 19, 2026Mathematische Zeitschrift0 citationsOpen Access

An abstract approach to algebras of braids and ties

RFRiccardo FasanoOspedale Garibaldi DFDomenico FiorenzaUniversity of Pisa PPPaolo PapiSapienza University of Rome

Key Points

To unify and generalize the existing types of braid and tie algebras in literature, including new variants.
Constructed algebras using approaches based on previous work by Marin.
Considered existing braids and ties algebras and their properties for the construction of new ones.
Developed a comprehensive framework for understanding various braid and tie algebras.
Introduced new algebras alongside generalizations of established ones.

Abstract

Abstract Generalizing work of Marin (Artin groups and Yokonuma–Hecke algebras. Int Math Res Not IMRN 13:4022–4062, 2018), we construct in a unified way all the “braids and ties” algebras available in literature and new ones.

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