Jane Arledge, Marcelo Laca and Iain Raeburn

摘要

Recently Bost and Connes considered a Hecke$C^*$-algebra arising from the ring inclusion of $Bbb Z$ in $Bbb Q$,and a $C^*$-dynamical system involving this algebra.Laca and Raeburn realized this algebra as a semigroup crossed product,and studied it using techniques they had previouslydeveloped for studying Toeplitz algebras. Here we associate Hecke algebras togeneral number fields, realize them as semigroup crossed products, and analyzetheir representations.