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Usually quantum chains with quantum group symmetry are associated with
representations of quantized universal algebras $U_q(g)$. Here we propose a
method for constructing quantum chains with $C_q(G)$ global symmetry, where
$C_q(G)$ is the algebra of functions on the quantum group. In particular we
will construct a quantum chain with $GL_q(2)$ symmetry which interpolates
between two classical Ising chains. It is shown that the Hamiltonian of this
chain satisfies the generalized braid group algebra.
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