Faithful representations of crossed products by actions of N^k - Larsen, N. S.; Raeburn, Iain (Mathematica Scandinavica, 2001)
We study a family of semigroup crossed products arising from actions of N^k by endomorphisms of groups. These include the Hecke algebra arising in the Bost-Connes analysis of phase transitions in number theory, and other Hecke algebras considered by Brenken. Our main theorem is a characterisation of the faithful representations of these crossed products, and generalises a similar theorem for the Bost-Connes algebra due to Laca and Raeburn.