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

  • N. S. Larsen
  • Iain Raeburn

Abstract

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.
Published
2001-12-01
How to Cite
Larsen, N. S., & Raeburn, I. (2001). Faithful representations of crossed products by actions of $\boldsymbol N^k$. MATHEMATICA SCANDINAVICA, 89(2), 283-296. https://doi.org/10.7146/math.scand.a-14342
Section
Articles