  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
consider a class of local (tensor space/functor) representations of the braid
group derived from a meld of the (non-functor) Burau representation and the
(functor) Deguchi {\em et al}-Kauffman--Saleur-Rittenberg representations here
called Burau-Rittenberg representations. In its most supersymmetric case
somewhat mystical cancellations of anomalies occur so that the Burau-Rittenberg
representation extends to a loop Burau-Rittenberg representation. And this
factors through $LH_n$. Let $SP_n$ denote the corresponding quotient algebra,
$k$ the ground ring, and $t \in k$ the loop-Hecke parameter. We prove the
following:
  1) $LH_n$ is finite dimensional over a field.
  2) The natural inclusion $LB_n \rightarrow LB_{n+1}$ passes to an inclusion
$SP_n \rightarrow SP_{n+1}$.
  3) Over $k=\mathbb{C}$, $SP_n / rad $ is generically the sum of simple matrix
algebras of dimension (and Bratteli diagram) given by Pascal's triangle.
  4) We determine the other fundamental invariants of $SP_n$ representation
theory: the Cartan decomposition matrix; and the quiver, which is of type-A.
  5) The structure of $SP_n $ is independent of the parameter $t$, except for
$t= 1$. \item For $t^2 \neq 1$ then $LH_n \cong SP_n$ at least up to rank$n=7$
(for $t=-1$ they are not isomorphic for $n>2$; for $t=1$ they are not
isomorphic for $n>1$).
  Finally we discuss a number of other intriguing points arising from this
construction in topology, representation theory and combinatorics.
