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Isomorphisms of unitary forms of Kac–Moody groups over finite fields
No full textAbstractWe use the methods developed in [Pierre-Emmanuel Caprace, “Abstract” homomorphisms of split Kac–Moody groups, Mem. Amer. Math. Soc. 198 (2009); Pierre-Emmanuel Caprace, Bernhard Mühlherr, Isomorphisms of Kac–Moody groups, Invent. Math. 161 (2005) 361–388; Pierre-Emmanuel Caprace, Bernhard Mühlherr, Isomorphisms of Kac–Moody groups which preserve bounded subgroups, Adv. Math. 206 (2006) 250–278] to solve the isomorphism problem of unitary forms of infinite split Kac–Moody groups over finite fields of square order
The isomorphism problem for almost split Kac-Moody groups
No full textZerfallende Kac-Moody-Gruppen wurden 1987 von Jacques Tits definiert, Bertrand Remy gab 1999 eine Definition von fast-zerfallenden Kac-Moody-Gruppen an, die mittels Galois-Abstieg von zerfallenden Kac-Moody-Gruppen konstruiert werden können. In der vorliegenden Arbeit wird das Isomorphieproblem für 2-sphärische fast-zerfallende Kac-Moody-Gruppen über Körpern der Charakteristik 0 gelöst. Wichtige Hilfsmittel dabei sind die Konstruktion von maximal zerfallenden Untergruppen und das detaillierte Studium von beschränkten Untergruppen. Die dabei erzielten Resultate verallgemeinern Ergebnisse von Armand Borel und Jacques Tits sowie Ergebnisse von Pierre-Emmanuel Caprace
On conjugacy separability of some Coxeter groups and parabolic-preserving automorphisms
No full textWe prove that even Coxeter groups, whose Coxeter diagrams contain no (4, 4, 2) triangles, are conjugacy separable. In particular, this applies to all right-angled Coxeter groups or word hyperbolic even Coxeter groups. For an arbitrary Coxeter group W, we also study the relationship between Coxeter generating sets that give rise to the same collection of parabolic subgroups. As an application we show that if an automorphism of W preserves the conjugacy class of every sufficiently short element then it is inner. We then derive consequences for the outer automorphism groups of Coxeter groups
The isomorphism problem for almost split Kac-Moody groups
No full textZerfallende Kac-Moody-Gruppen wurden 1987 von Jacques Tits definiert, Bertrand Remy gab 1999 eine Definition von fast-zerfallenden Kac-Moody-Gruppen an, die mittels Galois-Abstieg von zerfallenden Kac-Moody-Gruppen konstruiert werden können. In der vorliegenden Arbeit wird das Isomorphieproblem für 2-sphärische fast-zerfallende Kac-Moody-Gruppen über Körpern der Charakteristik 0 gelöst. Wichtige Hilfsmittel dabei sind die Konstruktion von maximal zerfallenden Untergruppen und das detaillierte Studium von beschränkten Untergruppen. Die dabei erzielten Resultate verallgemeinern Ergebnisse von Armand Borel und Jacques Tits sowie Ergebnisse von Pierre-Emmanuel Caprace
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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