A note on unitary polarities in finite Dickson semifield planes (Q2352480)

The present paper is an addendum to [\textit{A. M. W. Hui} et al., J. Geom. 104, No. 3, 469--493 (2013; Zbl 1302.51003)] and proves that ``any unitary polarity of the Dickson semifield plane \(\Pi({\mathcal K})\) is determined by an autotopism of the Dickson semifield \({\mathcal K}\) of the form \((\alpha,a\alpha,a^{-1}\alpha)\) for \(\alpha\) an involutory automorphism of \({\mathcal K}\) and \(a\in\mathbb{F}_q^*\), and that any unitary polarity defined by \((\alpha,a\alpha,a^{-1}\alpha)\) is conjugate to the one defined by \((\alpha,\alpha,\alpha)\). Thus, there is only one class of polar unitals in each of these planes.''