Orthogonal maximal abelian *-subalgebras of the 6x6 matrices

الأصل · EN

We construct new pairs of orthogonal maximal abelian *-subalgebras of M₆(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.