Translation spreads of the split Cayley hexagon

2003 ◽  
Vol 3 (2) ◽  
Author(s):  
Alan Offer
Keyword(s):  
Split Cayley Hexagon

scholarly journals Characterizations of the $G_2(4)$ and $L_3(4)$ Near Octagons

10.37236/8476 ◽  
2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Generalized Quadrangle ◽  
Line Geometry ◽  
Near Polygon ◽  
Generalized Polygon ◽  
Generalized Hexagon ◽  
Split Cayley Hexagon ◽  
Point Line ◽  
Line Spread

A triple $(\mathcal{S},S,\mathcal{Q})$ consisting of a near polygon $\mathcal{S}$, a line spread $S$ of $\mathcal{S}$ and a set $\mathcal{Q}$ of quads of $\mathcal{S}$ is called a polygonal triple if certain nice properties are satisfied, among which there is the requirement that the point-line geometry $\mathcal{S}'$ formed by the lines of $S$ and the quads of $\mathcal{Q}$ is itself also a near polygon. This paper addresses the problem of classifying all near polygons $\mathcal{S}$ that admit a polygonal triple $(\mathcal{S},S,\mathcal{Q})$ for which a given generalized polygon $\mathcal{S}'$ is the associated near polygon. We obtain several nonexistence results and show that the $G_2(4)$ and $L_3(4)$ near octagons are the unique near octagons that admit polygonal triples whose quads are isomorphic to the generalized quadrangle $W(2)$ and whose associated near polygons are respectively isomorphic to the dual split Cayley hexagon $H^D(4)$ and the unique generalized hexagon of order $(4,1)$.

scholarly journals Distinguished three-qubit ‘magicity’ via automorphisms of the split Cayley hexagon

2013 ◽  
Vol 12 (7) ◽  
pp. 2535-2549 ◽  
Author(s):  
Michel Planat ◽  
Metod Saniga ◽  
Frédéric Holweck
Keyword(s):  
Split Cayley Hexagon

scholarly journals Three-qubit operators, the split Cayley hexagon of order two, and black holes

2008 ◽  
Vol 78 (12) ◽  
Author(s):  
Péter Lévay ◽  
Metod Saniga ◽  
Péter Vrana
Keyword(s):  
Black Holes ◽  
Split Cayley Hexagon
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