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Canonical tensor product subfactors (CTPSs) describe, among other things, the embedding of chiral observables in two-dimensional conformal quantum field theories. A new class of CTPSs is constructed some of which are associated with certain modular invariants, thereby establishing the expected existence of the corresponding two-dimensional theories.
The program of matrix product states on the infinite tensor product ${mathcal A}^{otimes mathbb Z}$, initiated by Fannes, Nachtergaele and Werner in their seminal paper Commun. Math. Phys. Vol. 144, 443-490 (1992), is re-assessed in a context where $
For a discrete group $G$, we develop a `$G$-balanced tensor product of two coactions $(A,delta)$ and $(B,epsilon)$, which takes place on a certain subalgebra of the maximal tensor product $Aotimes_{max} B$. Our motivation for this is that we are able
We construct analogs of the embedding of orthogonal and symplectic groups into unitary groups in the context of fusion categories. At least some of the resulting module categories also appear in boundary conformal field theory. We determine when thes
Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar algebra, present
Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes non-rational th