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Characterizations by automorphism groups of some rank 3 buildings - IV: Hyperbolic p-adic Moufang buildings of rank 3 ; Van Steen, Kristel in Geometriae Dedicata (1999), 75(2), 115-122 In this paper, we introduce the p-adic Moufang condition for hyperbolic buildings of rank 3. It is the most obvious and simplest generalization of the p-adic Moufang condition for affine buildings ... [more ▼] In this paper, we introduce the p-adic Moufang condition for hyperbolic buildings of rank 3. It is the most obvious and simplest generalization of the p-adic Moufang condition for affine buildings, introduced in Part III of this sequence of papers. We show that p is very restricted, which confirms (but does not prove) the conjecture that no p-adic analogue is possible for the construction of Moufang (hyperbolic) buildings by Ronan and Tits. [less ▲] Detailed reference viewed: 7 (2 ULg)Characterizations by automorphism groups of some rank 3 buildings - II: A half strongly-transitive locally finite triangle building is a Bruhat-Tits building ; Van Steen, Kristel in Geometriae Dedicata (1999), 74(2), 113-133 We complete the proof of the fact that every locally finite triangle building Delta with a half strongly-transitive automorphism group G (e.g., this happens when Delta is defined via a (B, N)-pair in G ... [more ▼] We complete the proof of the fact that every locally finite triangle building Delta with a half strongly-transitive automorphism group G (e.g., this happens when Delta is defined via a (B, N)-pair in G) is a Bruhat-Tits building associated with a classical linear group over a locally finite local skewfield. [less ▲] Detailed reference viewed: 7 (1 ULg)Characterizations by automorphism groups of some rank 3 buildings, III. Moufang-like conditions Van Steen, Kristel in Geometriae Dedicata (1999), 74(3), 225-240 In this paper, we introduce the root-Moufang condition and the p-adic Moufang condition. We show that affine buildings of type (A) over tilde(2) satisfying the root-Moufang condition are Bruhat-Tits ... [more ▼] In this paper, we introduce the root-Moufang condition and the p-adic Moufang condition. We show that affine buildings of type (A) over tilde(2) satisfying the root-Moufang condition are Bruhat-Tits buildings. Also, every rank 3 affine building satisfying the p-adic Moufang condition is a Bruhat-Tits building. We motivate the introduction of the new conditions by showing that all Bruhat-Tits (A) over tilde(2)-buildings satisfy the root-Moufang condition, and that the (A) over tilde(2)-buildings over a p-adic field also satisfy the p-adic Moufang condition. Another application of the p-adic Moufang condition is given in Part IV of this paper. [less ▲] Detailed reference viewed: 4 (2 ULg)Characterizations by automorphism groups of some rank 3 buildings - I. Some properties of half strongly-transitive triangle buildings ; Van Steen, Kristel in Geometriae Dedicata (1998), 73(2), 119-142 In a sequence of papers, we will show that the existence of a (half) strongly-transitive automorphism group acting on a locally finite triangle building Delta forces Delta to be one of the examples ... [more ▼] In a sequence of papers, we will show that the existence of a (half) strongly-transitive automorphism group acting on a locally finite triangle building Delta forces Delta to be one of the examples arising from PSL3(K) for a locally finite local skewfield K. Furthermore, we introduce some Moufang-like conditions in affine buildings of rank 3, and characterize those examples arising from algebraic,classical or mixed type groups over a local field. In particular, we characterize the p-adic-like affine rank 3 buildings by a certain p-adic Moufang condition, and show that such a condition has zero probability to survive in hyperbolic rank 3 buildings. This shows that a construction of hyperbolic buildings as analogues of p-adic affine buildings is very unlikely to exist. Mathematics Subject Classifications (1991): 51E24, 51C05. [less ▲] Detailed reference viewed: 8 (2 ULg) |
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