@article{Larsen_Raeburn_2001, title={Faithful representations of crossed products by actions of $\boldsymbol N^k$}, volume={89}, url={https://www.mscand.dk/article/view/14342}, DOI={10.7146/math.scand.a-14342}, abstractNote={We study a family of semigroup crossed products arising from actions of $\boldsymbol N^k$ 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.}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Larsen, N. S. and Raeburn, Iain}, year={2001}, month={Dec.}, pages={283–296} }