ABSTRACT
In this chapter we introduce one of the most powerful techniques, ‘algebraic lifting’, for ‘generating new line spreads from old’. It might be regarded as the only known recursive process available for constructing projective planes: in the finite case one ‘lifts’ any given two-dimensional translation planes pi of (square) order n to another two-dimensional translation plane pi′ of order n2, and this process may be repeated as long as desired. Moreover, at each stage the lifted plane depends on the choice of coordinates so that even a one-step lift usually leads to a large number of non-isomorphic translation planes.
