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On the structure of quantum permutation groups

Teodor Banica·Sergiu Moroianu
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Abstract

The quantum permutation group of the set $X_n=\{1,..., n\}$ corresponds to the Hopf algebra $A_{aut}(X_n)$. This is an algebra constructed with generators and relations, known to be isomorphic to $\cc (S_n)$ for $n\leq 3$, and to be infinite dimensional for $n\geq 4$. In this paper we find an explicit representation of the algebra $A_{aut}(X_n)$, related to Clifford algebras. For $n=4$ the representation is faithful in the discrete quantum group sense.

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Teodor Banica, Sergiu Moroianu. 2005-07-28. On the structure of quantum permutation groups. https://arxiv.org/abs/math/0411576

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