Abstract Homomorphisms of Split Kac Moody Groups is popular PDF and ePub book, written by Pierre-Emmanuel Caprace in 2009-03-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Abstract Homomorphisms of Split Kac Moody Groups can be Read Online from any device for your convenience.
Abstract Homomorphisms of Split Kac Moody Groups Book PDF Summary
This work is devoted to the isomorphism problem for split Kac-Moody groups over arbitrary fields. This problem turns out to be a special case of a more general problem, which consists in determining homomorphisms of isotropic semisimple algebraic groups to Kac-Moody groups, whose image is bounded. Since Kac-Moody groups possess natural actions on twin buildings, and since their bounded subgroups can be characterized by fixed point properties for these actions, the latter is actually a rigidity problem for algebraic group actions on twin buildings. The author establishes some partial rigidity results, which we use to prove an isomorphism theorem for Kac-Moody groups over arbitrary fields of cardinality at least $4$. In particular, he obtains a detailed description of automorphisms of Kac-Moody groups. This provides a complete understanding of the structure of the automorphism group of Kac-Moody groups over ground fields of characteristic $0$. The same arguments allow to treat unitary forms of complex Kac-Moody groups. In particular, the author shows that the Hausdorff topology that these groups carry is an invariant of the abstract group structure. Finally, the author proves the non-existence of cocentral homomorphisms of Kac-Moody groups of indefinite type over infinite fields with finite-dimensional target. This provides a partial solution to the linearity problem for Kac-Moody groups.
Detail Book of Abstract Homomorphisms of Split Kac Moody Groups PDF
- Author : Pierre-Emmanuel Caprace
- Release : 06 March 2009
- Publisher : American Mathematical Soc.
- ISBN : 9780821842584
- Genre : Mathematics
- Total Page : 108 pages
- Language : English
- PDF File Size : 21,7 Mb
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