A generalization of Jaeger-Nomura's Bose Mesner algebra associated to type II matrices

Makoto Matsumoto

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 3, page 1027-1035
  • ISSN: 0373-0956

Abstract

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A category N generalizing Jaeger-Nomura algebra associated to a spin model is given. It is used to prove some equivalence among the four conditions by Jaeger-Nomura for spin models of index 2.

How to cite

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Matsumoto, Makoto. "A generalization of Jaeger-Nomura's Bose Mesner algebra associated to type II matrices." Annales de l'institut Fourier 49.3 (1999): 1027-1035. <http://eudml.org/doc/75354>.

@article{Matsumoto1999,
abstract = {A category $N$ generalizing Jaeger-Nomura algebra associated to a spin model is given. It is used to prove some equivalence among the four conditions by Jaeger-Nomura for spin models of index 2.},
author = {Matsumoto, Makoto},
journal = {Annales de l'institut Fourier},
keywords = {Bose-Mesner algebra; spin model; Jaeger-Nomura algebra; type II matrix; association scheme; link invariant},
language = {eng},
number = {3},
pages = {1027-1035},
publisher = {Association des Annales de l'Institut Fourier},
title = {A generalization of Jaeger-Nomura's Bose Mesner algebra associated to type II matrices},
url = {http://eudml.org/doc/75354},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Matsumoto, Makoto
TI - A generalization of Jaeger-Nomura's Bose Mesner algebra associated to type II matrices
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 3
SP - 1027
EP - 1035
AB - A category $N$ generalizing Jaeger-Nomura algebra associated to a spin model is given. It is used to prove some equivalence among the four conditions by Jaeger-Nomura for spin models of index 2.
LA - eng
KW - Bose-Mesner algebra; spin model; Jaeger-Nomura algebra; type II matrix; association scheme; link invariant
UR - http://eudml.org/doc/75354
ER -

References

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  1. [1] EI. BANNAI and ET. BANNAI, Generalized generalized spin models (four-weight spin models), Pac. J. Math., 170 (1995), 1-16. Zbl0848.05072MR97f:57005
  2. [2] T. HUANG and H. GUO, Four-weight spin models and related Bose-Mener algebras, preprint 1997. 
  3. [3] F. JAEGER, A talk in RIMS, 1994. 
  4. [4] F. JAEGER, M. MATSUMOTO and K. NOMURA, Bose-Mesner algebras related with type II matrices and spin models, Journal of Algebraic Combinatorics, 8 (1998), 39-72. Zbl0974.05084MR99f:05125
  5. [5] F. JAEGER and K. NOMURA, Symmetric versus non-symmetric spin models for link invariants, submitted (1997). Zbl0946.05084
  6. [6] V.F.R. JONES, On knot invariants related to some statistical mechanical models, Pac. J. Math., 137 (1989), 311-336. Zbl0695.46029MR89m:57005
  7. [7] K. NOMURA, An algebra associated with a spin model, Journal of Algebraic Combinatorics, 6 (1997), 53-58. Zbl0865.05077MR98g:05158

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