  Based on the Temperley--Lieb algebra we define a class of one-dimensional
Hamiltonians with nearest and next-nearest neighbour interactions. Using the
regular representation we give ground states of this model as words of the
algebra. Two point correlation functions can be computed employing the
Temperley--Lieb relations. Choosing a spin-1/2 representation of the algebra we
obtain a generalization of the (q-deformed) Majumdar--Ghosh model. The ground
states become valence-bond states.
