LAP Lambert Academic Publishing ( 02.12.2010 )
€ 59,00
In this thesis we deal with questions of continuous group cohomology of continuous representations of a separable locally compact group on a real or complex Banach space. Of particular importance is the case of a compact group. Here we use affine actions to prove vanishing theorems. To do this, we give an alternative definition of the cohomology, which is recursive. As a consequence we prove under certain conditions (equivalent with the existence of a non-trivial simultaneous fixed point of the associated affine map) all cohomology groups vanish. When G is a connected Lie group, we study the relationship of its cohomology with the corresponding Lie algebra cohomology. Finally, we consider the situation of a closed subgroup H of G which is cocompact and of cofinite volume and show just as in the case of a compact group that the restriction map H^n(G,V)-->H^n(H,V) is injective and apply this to questions of complete reducibility of representations.
Kitap detayları: |
|
ISBN-13: |
978-3-8433-7777-5 |
ISBN-10: |
3843377774 |
EAN: |
9783843377775 |
Kitabın dili: |
English |
Yazar: |
Ioannis Farmakis |
Sayfa sayısı: |
140 |
Yayın tarihi: |
02.12.2010 |
Kategori: |
Aritmetik, cebir |