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Pavages de l'espace affine

Abstract : For every odd positive integer d, we construct a fundamental domain for the action on the 2d+1-dimensional space of certain groups of affine transformations which are free, nonabelian, act properly discontinuously and have linear part Zariski-dense in SO(d+1,d). Next for every semisimple noncompact real Lie group G, we construct a group of affine transformations of its Lie algebra g which is free, nonabelian, acts properly discontinuously and has linear part Zariski-dense in Ad G. Finally, we give some results about the local behavior of harmonic functions on the Sierpinski triangle restricted to a side of the triangle.
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Ilia Smilga. Pavages de l'espace affine. Théorie des groupes [math.GR]. Université Paris Sud - Paris XI, 2014. Français. ⟨NNT : 2014PA112298⟩. ⟨tel-01127044⟩

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