Wild Kronecker quivers and amenability
Eckert, Sebastian
Eckert
Sebastian
We apply the notion of hyperfinite families of modules to the wild path
algebras of generalised Kronecker quivers $k\Theta(d)$. While the preprojective
and postinjective component are hyperfinite, we show the existence of a family
of non-hyperfinite modules in the regular component for some $d$. Making use of
dimension expanders to achieve this, our construction is more explicit than
previous results. From this it follows that no finitely controlled wild algebra
is of amenable representation type.
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2022