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Theorems of Helemskii and Johnson, revisited
Theo Buehler (ETHZ)
03.03.2008
Abstract:
The first homological characterizations of amenable groups were given
simultaneously by Helemskii and Johnson in the early seventies.
Helemskii's result reads: a group G is amenable if and only if the
ground field is injective in the category of Banach G-modules. Johnson
proved that a group is amenable if and only if the bounded cohomology
with coefficients in dual Banach G-modules vanishes outside degree
zero. We will explain why these results are just reformulations of each
other and give a simple proof based on the theory of derived functors.
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