Hjelmslev-quadrangles of level n

AbstractA Hjelmslev-quadrangle of level n is a rank 2 incidence structure having an ordinary generalized quadrangle as homomorphic image and satisfying some uniformity axioms. We show that certain infinite sequences of homomorphic Hjelmslev-quadrangles define an affine building of type C̃2. This is similar to the fact that sequences of projective Hjelmslev planes give rise to affine buildings of type Ã2. This analogy is emphasized by the fact that the inverse limit of the above sequences is proven to be an infinite generalized quadrangle