are not allowed, though they preserve the form (in terms of and these are and ; the additional "" in the hyperbolic case (as compared with the circular case) is necessary to specify the identity component because the group has connected components, while the group has components: has components, while only has 1. The fact that the squeeze transforms preserve area and orientation corresponds to the inclusion of subgroups – in this case – of the subgroup of hyperbolic rotations in the special linear group of transforms preserving area and orientation (a volume form). In the language of Möbius transformations, the squeeze transformations are the hyperbolic elements in the classification of elements.