%0 Journal Article
%T Half-commutative orthogonal Hopf algebras
%A Julien Bichon
%A Michel Dubois-Violette
%J Mathematics
%D 2012
%I arXiv
%X A half-commutative orthogonal Hopf algebra is a Hopf *-algebra generated by the self-adjoint coefficients of an orthogonal matrix corepresentation $v=(v_{ij})$ that half commute in the sense that $abc=cba$ for any $a,b,c \in \{v_{ij}\}$. The first non-trivial such Hopf algebras were discovered by Banica and Speicher. We propose a general procedure, based on a crossed product construction, that associates to a self-transpose compact subgroup $G \subset U_n$ a half-commutative orthogonal Hopf algebra $\mathcal A_*(G)$. It is shown that any half-commutative orthogonal Hopf algebra arises in this way. The fusion rules of $\mathcal A_*(G)$ are expressed in term of those of $G$.
%U http://arxiv.org/abs/1202.5120v1