# 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} }

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…

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