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Samson Abramsky Temperley-Lieb Algebra

Summary: Samson Abramsky
Temperley-Lieb Algebra:
From Knot Theory to
Logic and Computation
via Quantum Mechanics
1 Introduction
Our aim in this paper is to trace some of the surprising and beau-
tiful connections which are beginning to emerge between a number of
apparently disparate topics.
1.1 Knot Theory
Vaughan Jones' discovery of his new polynomial invariant of knots in
1984 [26] triggered a spate of mathematical developments relating knot
theory, topological quantum field theory, and statistical physics inter
alia [44, 30]. A central r^ole, both in the initial work by Jones and in the
subsequent developments, was played by what has come to be known as
the Temperley-Lieb algebra.1
1.2 Categorical Quantum Mechanics
Recently, motivated by the needs of Quantum Information and Com-
putation, Abramsky and Coecke have recast the foundations of Quantum
Mechanics itself, in the more abstract language of category theory. The


Source: Abramsky, Samson - Computing Laboratory, University of Oxford


Collections: Computer Technologies and Information Sciences