Orthogonal maximal abelian *-subalgebras of the 6x6 matrices

2006/09/03 by Kyle A. Beauchamp, Kyle Beauchamp, Beauchamp, Kyle +3 · 4 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Photonic Communication Systems #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Optical Network Technologies #Quantum Physics (quant-ph) #graph theory and CDMA systems #math.CO #math.OA #quant-ph

paper · pdf · doi:10.48550/arxiv.math/0609076

arxiv created 2006/09/03 · openalex publication_date 2006/09/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct new pairs of orthogonal maximal abelian *-subalgebras of M₆(\mathbb C), by classifying all self-adjoint complex Hadamard matrices of order 6. In particular, we exhibit a non-affine one-parameter family of non-equivalent Hadamard matrices of order 6. In the last part of the paper we present other previously unknown examples of complex Hadamard matrices of higher orders.

Citations

• Some results on the parametrization of complex Hadamard matrices

Cited by

• Equivalence of complex Hadamard matrices
• Non-affine Families of 8 x 8 Complex Hadamard Matrices
• Subfactors and Hadamard Matrices
• Constructing mutually unbiased bases in dimension six

Related

• On Generalized Hadamard Matrices and Difference Matrices: Z₆
• Towards a classification of 6× 6 complex Hadamard matrices
• Some special complex Hadamard matrices of order six
• Four-parameter families of complex Hadamard matrices of order six
• A two-parameter family of complex Hadamard matrices of order 6 induced by hypocycloids