In this chapter we apply the Lie algebraic approach to the symmetric inclusion processes. This is a process describing particles that move on a lattice with an attractive interaction. We show that the generator of this process can be written in an abstract form in terms of the generators of the Lie algebra \(\mathfrak {su}(1,1)\) . This allows to easily find symmetries of the generator. Applying these symmetries to the cheap self-duality function related to the reversible product measures, we find a non-trivial triangular self-duality function. We then show how the same result can be obtained via the change-of-representation method. As an application of this self-duality result we show how the self-duality relation provides information about the n-point correlations. In particular we show that, starting from local-equilibrium measures, the time-evolved measure under the inclusion dynamics has positive correlations.