Symmetric versus non-symmetric spin models for link invariants
type: Item
instance of: scholarly article
title: Symmetric versus non-symmetric spin models for link invariants
zbMATH Open document ID: 0946.05084
DOI: 10.1023/A:1018771332556
author: François Jaeger
author: Kazumasa Nomura
published in: Journal of Algebraic Combinatorics
publication date: 2000-03-30T00:00:00Z
review text: In [Pac. J. Math. 137, No. 2, 311-334 (1989; Zbl 0695.46029)] V. F. R. Jones introduced the notion of a spin model and associated a complex number to it which is a link invariant. A spin model is a triple \((X, w_+, w_-)\) where \(X\) is a finite set and \(w_+\) and \(w_-\) are complex matrices with rows and columns indexed by \(X\). In the definition of Jones these matrices are symmetric. The first author used in [Geom. Dedicata 44, No. 1, 23-52 (1992; Zbl 0773.57005)] association schemes to construct spin models which has led to a generalization to non-symmetric matrices. The link invariants associated to symmetric spin models depend only trivially on the orientation of the link. In this paper non-symmetric Hadamard spin modules are defined which give the first known examples of a non-symmetric spin model where the associated link invariants depend non-trivially on the orientation of the link.
reviewed by: Barbara Baumeister
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1389485
zbMATH Keywords: link invariant
zbMATH Keywords: spin model
zbMATH Keywords: association schemes
MaRDI profile type: Publication
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full work available at URL: a:1018771332556
OpenAlex ID: W107670886
description: scientific article; zbMATH DE number 1389485