Year: 2013
Type: article
Abstract: We classify up to conjugacy the subgroups of certain types in the full, in the affine, and in the special affine Cremona groups.We prove that the normalizers of these subgroups are algebraic.As an application, we obtain new results in the Linearization Problem generalizing to disconnected groups Bia lynicki-Birula's results of 1966-67.We prove "fusion theorems" for n-dimensional tori in the affine and in the special affine Cremona groups of rank n.In the final section we introduce and discuss the notions of Jordan decomposition and torsion primes for the Cremona groups.
Source: Izvestiya Mathematics
Author: V L Popov
Institutions: Russian Academy of Sciences, Steklov Mathematical Institute
Language: ceb
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2102743161