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Article Dans Une Revue Pacific Journal of Mathematics Année : 2013

Half-commutative orthogonal Hopf algebras

Résumé

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 $G$.
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Dates et versions

hal-00673133 , version 1 (22-02-2012)

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Citer

Julien Bichon, Michel Dubois-Violette. Half-commutative orthogonal Hopf algebras. Pacific Journal of Mathematics, 2013, 263 (1), pp.13-28. ⟨hal-00673133⟩
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