The Veldkamp Space of GQ(2,4)

0357074 - ÚFCH JH 2011 RIV SG eng J - Journal Article
Saniga, M. - Green, R. M. - Levay, P. - Vrana, P. - Pracna, Petr
The Veldkamp Space of GQ(2,4).
International Journal of geometric Methods in Modern Physics. Roč. 7, č. 7 (2010), s. 1133-1145. ISSN 0219-8878. E-ISSN 1793-6977
Grant - others:VEGA(XE) 2/7012/27; VEGA(XE) 2/0092/09; VEGA(XE) 2/0098/10
Institutional research plan: CEZ:AV0Z40400503
Keywords : GQ(2,4) * Veldkamp space * 3-qubits/2-qutrits
Subject RIV: CF - Physical ; Theoretical Chemistry
Impact factor: 0.757, year: 2010

It is shown that the Veldkamp space of the unique generalized quadrangle GQ(2, 4) is isomorphic to PG(5, 2). Since the GQ(2, 4) features only two kinds of geometric hyperplanes, namely point's perp-sets and GQ(2, 2)s, the 63 points of PG(5, 2) split into two families; 27 being represented by perp-sets and 36 by GQ(2, 2) s. The 651 lines of PG(5, 2) are found to fall into four distinct classes: in particular, 45 of them feature only perp-sets, 216 comprise two perp-sets and one GQ(2, 2), 270 consist of one perp-set and two GQ(2, 2) s and the remaining 120 are composed solely of GQ(2, 2) s, according to the intersection of two distinct hyperplanes determining the (Veldkamp) line is, respectively, a line, an ovoid, a perp-set and a grid (i.e. GQ(2, 1)) of a copy of GQ(2, 2).
Permanent Link: http://hdl.handle.net/11104/0195438