Vol. 19, No. 2, 2022

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Classifying derivable nets

Norman L. Johnson

Vol. 19 (2022), No. 2, 59–94
Abstract

This article is a study of arbitrary derivable nets. These nets are known to be embeddable into 3-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
Mathematical Subject Classification
Primary: 51A05, 51A40
Milestones
Received: 9 November 2021
Accepted: 17 January 2022
Published: 28 May 2022
Authors
Norman L. Johnson
University of Iowa
United States