London Mathematical Society
Workshop on Limit Algebras
held at Ambleside and Lancaster
The workshop began on Monday 30^{th} June 1997 at the
University College of St.
Martins in Ambleside
and transfered to Lancaster University from the
5^{th} to the 13^{th} 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

Meetirreducible 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
 4cycle limit algebras and classifications by K_{0} +
H_{1}
 Christian Skau (Trondheim)
 The interplay between topological
dynamical systems and C*algebras, and
their Ktheoretic invariants I
 The interplay between topological
dynamical systems and C*algebras, and
their Ktheoretic invariants II
 Douglas Somerset (Aberdeen)
 The ideal structure of TAFalgebras.

Applications of the meetirreducible ideal space
of a TAF algebra
Other participants
 Rob Archbold (Aberdeen),
 Gordon Blower (Lancaster),
 Elliott Gootman (Georgia),
 Graham Jameson (Lancaster),
 Alastair King (Lancaster),
 Aldo Lazar (Tel Aviv),
 Marc Wasley (Lancaster),
 Alex Zaleskii (East Anglia).