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7 papers · 1 filter
Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers
Marcelo Laca, Iain Raeburn
We show that the group of orientation-preserving affine transformations of the rational numbers is quasi-lattice ordered by its subsemigroup ${\…
Hecke algebras from groups acting on trees and HNN extensions
Udo Baumgartner, Marcelo Laca, Jacqui Ramagge +1
We study Hecke algebras of groups acting on trees with respect to geometrically defined subgroups. In particular, we consider Hecke algebras of groups of automorphisms of locally f…
The Local Index Formula in Semifinite von Neumann Algebras II: The Even Case
Alan L. Carey, John Phillips, Adam Rennie +1
We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. The proof is a…
The Local Index Formula in Semifinite von Neumann Algebras I: Spectral Flow
Alan L. Carey, John Phillips, Adam Rennie +1
We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. In this setting it…
The Hochschild Class of the Chern Character For Semifinite Spectral Triples
A. Carey, J. Phillips, A. Rennie +1
We provide a proof of Connes' formula for a representative of the Hochschild class of the Chern character for (p,\infty)-summable spectral triples. Our proof is valid for all semif…
Subquotients of Hecke C^*-algebras
Nathan Brownlowe, Nadia S. Larsen, Ian F. Putnam +1
The Bost-Connes Hecke C^*-algebra can be regarded as a direct limit of subalgebras involving finite sets of primes. Each of these finite-prime analogues of the Bost-Connes algebra…