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.

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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