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Weak Hopf Algebras II: Representation theory, dimensions, and the Markov trace
 J. Algebra
"... If A is a weak C∗Hopf algebra then the category of finite dimensional unitary representations of A is a monoidal C∗category with monoidal unit being the GNS representation Dε associated to the counit ε. This category has isomorphic left dual and right dual objects which leads, as usual, to the not ..."
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Cited by 20 (3 self)
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If A is a weak C∗Hopf algebra then the category of finite dimensional unitary representations of A is a monoidal C∗category with monoidal unit being the GNS representation Dε associated to the counit ε. This category has isomorphic left dual and right dual objects which leads, as usual, to the notion of dimension function. However, if ε is not pure the dimension function is matrix valued with rows and columns labelled by the irreducibles contained in Dε. This happens precisely when the inclusions AL ⊂ A and AR ⊂ A are not connected. Still there exists a trace on A which is the Markov trace for both inclusions. We derive two numerical invariants for each C∗WHA of trivial hypercenter. These are the common indices I and δ, of the Haar, respectively Markov conditional expectations of either one of the inclusions AL/R ⊂ A and ÂL/R ⊂ Â. In generic cases I> δ. In the special case of weak Kac algebras we show that I = δ is an integer. Submitted to J. Algebra
Pseudo limits, biadjoints, and pseudo algebras: categorical foundations of conformal field theory
 Mem. Amer. Math. Soc
"... The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjun ..."
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Cited by 18 (8 self)
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The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjunction, are necessary for this
Restriction Categories I
 Categories of Partial Maps, Theoret. Comput. Sci
, 2006
"... modality”) and a differential combinator, satisfying a number of coherence conditions. In ..."
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Cited by 10 (1 self)
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modality”) and a differential combinator, satisfying a number of coherence conditions. In
unknown title
, 2006
"... modality”) and a differential combinator, satisfying a number of coherence conditions. In ..."
Abstract
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modality”) and a differential combinator, satisfying a number of coherence conditions. In