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The Veldkamp Space of GQ(2,4)
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SYSNO ASEP 0357074 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Veldkamp Space of GQ(2,4) Author(s) Saniga, M. (SK)
Green, R. M. (US)
Levay, P. (HU)
Vrana, P. (HU)
Pracna, Petr (UFCH-W)Source Title International Journal of geometric Methods in Modern Physics. - : World Scientific Publishing - ISSN 0219-8878
Roč. 7, č. 7 (2010), s. 1133-1145Number of pages 13 s. Language eng - English Country SG - Singapore Keywords GQ(2,4) ; Veldkamp space ; 3-qubits/2-qutrits Subject RIV CF - Physical ; Theoretical Chemistry CEZ AV0Z40400503 - UFCH-W (2005-2011) UT WOS 000285459200004 DOI https://doi.org/10.1142/S0219887810004762 Annotation 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). Workplace J. Heyrovsky Institute of Physical Chemistry Contact Michaela Knapová, michaela.knapova@jh-inst.cas.cz, Tel.: 266 053 196 Year of Publishing 2011
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