Is there a name for the algebra (and its tensor products) given by generators $U_{j}$, $j \in \mathbb{Z}_{n}$ 

under the conditions $U_{j} = (1 - U_{j-1})(1-U_{j+1})$? There is no restriction on the commutativity of $U_{j}$. I am interested in structures for all possible cases for $U_{j}$.