  Loop Quantum Gravity (LQG) is an attempt to describe the quantum gravity
regime. Introducing a non-zero cosmological constant $\Lambda$ in this context
has been a withstanding problem. Other approaches, such as Chern-Simons
gravity, suggest that quantum groups can be used to introduce $\Lambda$ in the
game. Not much is known when defining LQG with a quantum group. Tensor
operators can be used to construct observables in any type of discrete quantum
gauge theory with a classical/quantum gauge group. We illustrate this by
constructing explicitly geometric observables for LQG defined with a quantum
group and show for the first time that they encode a quantized hyperbolic
geometry. This is a novel argument pointing out the usefulness of quantum
groups as encoding a non-zero cosmological constant. We conclude by discussing
how tensor operators provide the right formalism to unlock the LQG formulation
with a non-zero cosmological constant.
