Locally compact (2, 2)‐transformation groups |
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| Authors: | Alfonso Di Bartolo Giovanni Falcone Karl Strambach |
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| Institution: | 1. Dipartimento di Matematica e Applicazioni, Via Archirafi 34, I‐90123 Palermo, Italy;2. Phone: +39 09123891071, Fax: +39 09123891024;3. Dipartimento di Metodi e Modelli Matematici, Viale delle Scienze Ed. 8, I‐90128 Palermo, Italy;4. Phone: +39 0916657328, Fax: +39 091427258;5. Department Mathematik, Bismarckstra?e 1 1/2, 91054 Erlangen, Germany |
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| Abstract: | We determine all locally compact imprimitive transformation groups acting sharply 2‐transitively on a non‐totally disconnected quotient space of blocks inducing on any block a sharply 2‐transitive group and satisfying the following condition: if Δ1, Δ2 are two distinct blocks and Pi, Qi ∈ Δi (i = 1, 2), then there is just one element in the inertia subgroup which maps Pi onto Qi. These groups are natural generalizations of the group of affine mappings of the line over the algebra of dual numbers over the field of real or complex numbers or over the skew‐field of quaternions. For imprimitive locally compact groups, our results correspond to the classical results of Kalscheuer for primitive locally compact groups (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Topological imprimitive transformation groups Kalscheuer near‐fields dual quaternions |
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