×

Nomura algebras of nonsymmetric Hadamard models. (English) Zbl 1245.05012

Summary: We show that the Nomura algebra of the nonsymmetric Hadamard model coincides with the Bose-Mesner algebra of the directed Hadamard graph.

MSC:

05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05E30 Association schemes, strongly regular graphs

References:

[1] Brouwer A.E., Cohen A.M., Neumaier A.: Distance-Regular Graphs. Springer-Verlag, Heidelberg (1989) · Zbl 0747.05073
[2] Bannai E., Ito T.: Algebraic combinatorics I. Benjamin/Cummings, Menlo Park (1984) · Zbl 0555.05019
[3] Higman D.G.: Coherent configurations. I. Rend. Sem. Mat. Univ. Padova 44, 1–25 (1970) · Zbl 0279.05025
[4] Jaeger F.: Strongly regular graphs and spin models for the Kauffman polynomial. Geom. Dedic. 44, 23–52 (1992) · Zbl 0773.57005 · doi:10.1007/BF00147743
[5] Jaeger F., Matsumoto M., Nomura K.: Bose–Mesner algebras related to type II matrices and spin models. J. Algebr. Combin. 8, 39–72 (1998) · Zbl 0974.05084 · doi:10.1023/A:1008691327727
[6] Jaeger F., Nomura K.: Symmetric versus non-symmetric spin models for link invariants. J. Algebr. Combin. 10, 241–278 (1999) · Zbl 0946.05084 · doi:10.1023/A:1018771332556
[7] Jones V.F.R.: On knot invariants related to some statistical mechanical models. Pac. J. Math. 137, 311–336 (1989) · Zbl 0695.46029 · doi:10.2140/pjm.1989.137.311
[8] Klin M., Muzychuk M., Pech C., Woldar A., Zieschang P.-H.: Association schemes on 28 points as mergings of a half-homogeneous coherent configuration. Eur. J. Combin. 28, 1994–2025 (2007) · Zbl 1145.05056 · doi:10.1016/j.ejc.2006.08.010
[9] Nomura K.: Spin models constructed from Hadamard matrices. J. Combin. Theory A 68, 251–261 (1994) · Zbl 0808.05100 · doi:10.1016/0097-3165(94)90106-6
[10] Nomura K.: An algebra associated with a spin model. J. Algebr. Combin. 6, 53–58 (1997) · Zbl 0865.05077 · doi:10.1023/A:1008644201287
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.