London Mathematical Society Workshop on Limit Algebras

held at Ambleside and Lancaster

The workshop began on Monday 30th June 1997 at the University College of St. Martins in Ambleside and transfered to Lancaster University from the 5th to the 13th July. The event brought together twenty specialists with interests in nonselfadjoint operator algebras, limit algebras and topological dynamical systems and the programme of three formal talks per day left useful periods of time for extensive discussion and interaction. The period in Lancaster made extensive library facilities available as well as providing a stimulating change of environment and in this phase of the workshop there was a participation of about fourteen specialists including all those with expertise in limit algebras and Cantor minimal systems. The programme of talks was organised by Stephen Power and assistance in running the workshop was given by Alan Hopenwasser who was visiting Lancaster University as an EPSRC Visiting Fellow. A number of key speakers gave two talks, presenting a preliminary view of the topic (in Ambleside) followed by a more detailed development (in Lancaster). Recent advances in the analysis of nonselfadjoint operator algebras were presented in the talks of Davidson, Donsig, Hopenwasser, Hudson, Peters, Pitts and Power. Banach algebra perspectives, on Hochschild cohomology and on the structure of ideals, were given in the talks of Lykova, Somerset and Hudson. Discussions with Zaleskii and King underlined the purely algebraic side of limit algebras and the deepening connections with locally finite algebras. An additional theme of the workshop centered on recent progress in the analysis of Cantor minimal systems and the interplay between dynamical invariants and C*-algebra invariants, as well as the specific cases for tilings, substitution systems and quasicrystals. The combinatorial and homological properties of ordered Bratteli diagrams provided a common ground here with the nonselfadjoint limit algebraists and the workshop was fortunate to have lucid expositions on these developments from Forrest, Kellendonk and Skau. The workshop aim of fostering new perspectives and exchanges seems to have been well met.

The Talks

Kenneth Davidson (Waterloo)
Nest algebras are hyperfinite
Principal bimodules of nest algebras
Alan Donsig (Lincoln, Nebraska)
Spectral characterisations of limit algebras
Meet-irreducible ideals
Alan Forrest (Trondheim)
Almost Finite Relations for Dynamical Systems
Dynamics on ordered Cantor sets
Alan Hopenwasser (Alabama)
The Fundamentals of Triangular Limit Algebras
Boundary functions for ideals
Timothy Hudson (East Carolina University)
Primitive Triangular UHF Algebras
Radicals and Ideals
Johannes Kellendonk (Berlin)
Topological equivalence of tilings
Zinaida Lykova (Newcastle)
Some methods of computing the cohomology of triangular algebras
Justin Peters (Iowa)
Semicrossed products of the Disk Algebra I
Semicrossed products of the Disk Algebra II
David Pitts (Nebraska)
Ideals in nest algebras
Stephen Power (Lancaster)
Dimension distribution groups
4-cycle limit algebras and classifications by K0 + H1
Christian Skau (Trondheim)
The interplay between topological dynamical systems and C*-algebras, and their K-theoretic invariants I
The interplay between topological dynamical systems and C*-algebras, and their K-theoretic invariants II
Douglas Somerset (Aberdeen)
The ideal structure of TAF-algebras.
Applications of the meet-irreducible ideal space of a TAF algebra

Other participants