Faithful representations of crossed products by actions of $\boldsymbol N^k$

N. S. Larsen, Iain Raeburn


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.

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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