Abstract Homomorphisms of Split Kac-Moody Groups (Memoirs of the American Mathematical Society 198, 924)
By: Pierre-Emmanuel Caprace (author)Paperback
1 - 2 weeks availability
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 semi simple 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 co central 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.
Number Of Pages:
- ID: 9780821842584
- Saver Delivery: Yes
- 1st Class Delivery: Yes
- Courier Delivery: Yes
- Store Delivery: Yes
Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly
© Copyright 2013 - 2016 WHSmith and its suppliers.
WHSmith High Street Limited Greenbridge Road, Swindon, Wiltshire, United Kingdom, SN3 3LD, VAT GB238 5548 36