Geodesic
On symmetrical $q$-extensions of the 2-dimensional grid
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 199-209

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In the paper, properties of symmetrical $q$-extensions of the grids are investigated. We obtain a criteria for sets of symmetrical $q$-extensions of the grid $\Lambda^2$ to be finite. Using this criteria we prove, in particular, that the set of all $Aut_0(\Lambda^2)$-symmetrical $q$-extensions of the grid $\Lambda^2$ is finite for any prime $q$. In addition, we give a list of all $Aut_0(\Lambda^2)$-symmetrical 3-extensions of the grid $\Lambda^2$.
Keywords: $d$-dimensional grids, symmetrical $q$-extensions. 
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     title = {On symmetrical $q$-extensions of the 2-dimensional grid},
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E. A. Neganova; V. I. Trofimov. On symmetrical $q$-extensions of the 2-dimensional grid. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 199-209. http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a21/