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Full-Text Articles in Physical Sciences and Mathematics
Affine Kac-Moody Groups Of Types Ii And Iii, Jacqueline Ramagge
Affine Kac-Moody Groups Of Types Ii And Iii, Jacqueline Ramagge
Professor Jacqui Ramagge
We announce a theorum which states that, over certain fields, affine Kac-Moody groups of types II and III arise as the fixed point subgroups under particular automorphism of affine Kac_moody groups obtained from a simply laced extended Cartan matrices (and hence of type I) of higher rank. Thus our result extends a theorum on Kac-Moody algebras to corresponding groups. A detailed proof of this result will appear in the J. Algebra.
On Certain Fixed Point Subgroups Of Affine Kac-Moody Groups, Jacqueline Ramagge
On Certain Fixed Point Subgroups Of Affine Kac-Moody Groups, Jacqueline Ramagge
Professor Jacqui Ramagge
In this paper we give a detailed description of the fixed point subgroups of certain Kac-Moody groups under particular automorphisms. We consider Kac-Moody groups arising from simply laced extended Cartan matrices and their fixed point subgroups under automorphisms which contain a non-trivial field automorphism constituent as well as a non-trivial graph automorphism constituent. We show that such a situation satisfies all the conditions of a theorem of J-Y. Hée "Torsion de groupes munis dune donnée radicelle, Théorème (4.5)" which concludes that the fixed point subgroup has a B , N )-pair and a system of root subgroups. This paper contains …
Cohomology Of Buildings And Finiteness Properties Of An-Groups, Jacqueline Ramagge, Wayne Wheeler
Cohomology Of Buildings And Finiteness Properties Of An-Groups, Jacqueline Ramagge, Wayne Wheeler
Professor Jacqui Ramagge
Borel and Serre calculated the cohomology of the building associated to a reductive group and used the result to deduce that torsion-free S-arithmetic groups are duality groups. By replacing their group-theoretic arguments with proofs relying only upon the geometry of buildings, we show that Borel and Serre's approach can be modied to calculate the cohomology of any locally nite ane building. As an application we show that any nitely presented e An-group is a virtual duality group. A number of other niteness conditions for e An-groups are also established.