This article is a study of arbitrary derivable nets. These nets are known to be embeddable into
-dimensional
projective spaces over skewfields, and may be represented as pseudo-regulus nets in a
classical manner. However, their typology is not well known. This article gives a
classification of derivable nets by comparing such nets to any given classical
pseudo-regulus net. There are four classes and examples of each are given. A number of
applications of this material are discussed.
Keywords
flocks of cones, twisted hyperbolic flocks, derivable nets,
translation planes, generalized quadrangles, quaternion
division rings, cyclic division rings, André and Ostrom
extensions
