• Corpus ID: 221095861

# Generalisations of Hecke algebras from Loop Braid Groups

@article{Damiani2020GeneralisationsOH,
title={Generalisations of Hecke algebras from Loop Braid Groups},
author={Celeste Damiani and Paul Purdon Martin and Eric C. Rowell},
journal={arXiv: Geometric Topology},
year={2020}
}
• Published 11 August 2020
• Mathematics
• arXiv: Geometric Topology
We introduce a generalisation $LH_n$ of the ordinary Hecke algebras informed by the loop braid group $LB_n$ and the extension of the Burau representation thereto. The ordinary Hecke algebra has many remarkable arithmetic and representation theoretic properties, and many applications. We show that $LH_n$ has analogues of several of these properties. In particular we introduce a class of local representations of the braid group derived from a meld of the Burau representation and the Rittenberg…
2 Citations

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