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Hopf Algebras and Subfactors Associated to Vertex Models

✍ Scribed by Teodor Banica

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
348 KB
Volume
159
Category
Article
ISSN
0022-1236

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✦ Synopsis

If H is a Hopf algebra whose square of the antipode is the identity, v # L(V) H is a corepresentation, and ?: H Γ„ L(W) is a representation, then u=(id ?) 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 equation arises in this way. A more elaborate construction shows that there exists a minimal'' triple (H, v, ?) satisfying (id ?) 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., S 2 {id) case.

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