ar X iv : 0 90 8 . 33 63 v 2 [ m at h - ph ] 1 S ep 2 00 9 Geometric Hyperplanes of the Near Hexagon L 3 × GQ ( 2 , 2 )
نویسندگان
چکیده
Having in mind their potential quantum physical applications, we classify all geometric hyperplanes of the near hexagon that is a direct product of a line of size three and the generalized quadrangle of order two. There are eight different kinds of them, totalling to 1023 = 2 10 − 1 = |PG(9, 2)|, and they form two distinct families intricately related with the points and lines of the Veldkamp space of the quadrangle in question.
منابع مشابه
ar X iv : 0 90 3 . 07 15 v 1 [ m at h - ph ] 4 M ar 2 00 9 The Veldkamp Space of GQ ( 2 , 4 )
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 parti...
متن کاملar X iv : 0 90 3 . 07 15 v 2 [ m at h - ph ] 6 J ul 2 00 9 The Veldkamp Space of GQ ( 2 , 4 )
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 parti...
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