Open AccessFaithful representations of crossed products by actions of $\boldsymbol N^k$
Author(s) -
Nadia S. Larsen,
Iain Raeburn
Publication year - 2001
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14342
Subject(s) - endomorphism , mathematics , hecke algebra , semigroup , pure mathematics , algebra over a field , structured program theorem
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.