Kernels of linear representations of Lie groups, locally compact groups, and pro-Lie Groups
-
Markus Stroppel
Abstract.
For a topological group 
the intersection 
of all
kernels of ordinary representations is studied. We show that
is contained in the center of 
if 
is a connected
pro-Lie group. The class 
is determined
explicitly if 
is the class of connected Lie groups or
the class of almost-connected Lie groups: in both cases, it consists
of all compactly-generated abelian Lie groups. Every compact
abelian group and every connected abelian pro-Lie group occurs as
for some connected pro-Lie group 
. However, the
dimension of 
is bounded by the cardinality of the continuum
if 
is locally compact and connected. Examples are given to show
that 
becomes complicated if 
contains groups with infinitely many connected components.
© 2012 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- 2-Blocks with minimal nonabelian defect groups II
- Rational defect groups and 2-rational characters, II
- On monotone 2-groups
- A note on a result of Skiba
- A focal subgroup theorem for outer commutator words
- Kernels of linear representations of Lie groups, locally compact groups, and pro-Lie Groups
- The fundamental group of a quotient of a product of curves
Articles in the same Issue
- Masthead
- 2-Blocks with minimal nonabelian defect groups II
- Rational defect groups and 2-rational characters, II
- On monotone 2-groups
- A note on a result of Skiba
- A focal subgroup theorem for outer commutator words
- Kernels of linear representations of Lie groups, locally compact groups, and pro-Lie Groups
- The fundamental group of a quotient of a product of curves
