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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 in the generalised braid group algebra. 0doi:10.1063/1.531372 fatcat:hqghyw5q6bddzlf7hnsqd6zfaa