1998/04/03 by Teodor Banica · 1 citation
Mathematics · #math.QA #math.OA
published as J. Funct. Anal. 159 (1998), 243-266 · 25 pages, Latex
arxiv created 1998/04/03 · arxiv updated 2009/11/30
If H is a Hopf algebra whose square of the antipode is the identity, v∈ł(V)⊗ H is a corepresentation, and π:H→ł(W) is a representation, then u=(id⊗π)v satisfies the equation (t⊗ id)u-1=((t⊗ id)u)-1 of the vertex models for subfactors. A universal construction shows that any solution u of this equatio n arises in this way. A more elaborate construction shows that there exists a ``minimal'' triple (H,v,π) satisfying (id⊗π)v=u. This paper is devoted to the study of this latter construction of Hopf algebras. If u is unitary we construct a \c^*-norm on H and we find a new description of the standard invariant of the subfactor associated to u. We discuss also the ``twisted'' (i.e. S2≠ id) case.