ABSTRACT

This chapter is a prelude to our study of algebraic lifting, Chapter 35. Algebraic lifting is a powerful recursive technique that converts (‘lifts’) line spreads in PG(3, q) to line spreads in PG(3, q2). We note that the term ‘lifting’ is used in this text three ways. In this chapter, ‘lifting’ shall refer to ‘algebraic lifting’. Actually, lifting is essentially an algebraic process that converts spread sets of 2 × 2 matrices over GF (q) to spread sets of 2× 2 matrix over GF (q2) by a purely algebraic procedure, and by recoordinatizing the same GF (q)-line-spread over by different spread sets one expects to lift to a range of possibly non-isomorphic line spreads over GF (q2). Hence, it becomes desirable to characterize lifted spread sets geometrically.