Abstract :
We develop a combinatorial approach to the quantum permutation algebras, as Hopf images of representations
of type π : As(n)→B(H). We discuss several general problems, including the commutativity
and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and the
Tannakian aspects of the construction. The main motivation comes from the quantum invariants of the complex
Hadamard matrices: we show here that, under suitable regularity assumptions, the computations can
be performed up to n = 6.
© 2009 Elsevier Inc. All rights reserved.
