Shigeru Yamagami

IRREDUCIBLE BIMODULES ASSOCIATED WITH CROSSED PRODUCT ALGEBRAS

Crossed-product factors F⋊Γ⊃F⋊H, F⋊K and bimodules naturally arising from them are considered. Basic properties of these bimodules (necessary to study inclusion relations of factors) are established together with some applications.

On unitary representation theories of compact quantum groups

Categorical structure of unitary representation of compact quantum groups is studied with relation to a metrical structure encountered in the monoidal category of bimodules of finite Jones index.

C∗-tensor categories and free product bimodules

Abstract A C ∗ -tensor category with simple unit object and countably many generators is realized by von Neumann algebra bimodules of finite Jones index if and only if it is rigid.

Group symmetry in tensor categories and duality for orbifolds

Abstract A duality for orbifolds is presented as an application of group extensions in tensor categories.

Notes on Amenability of Commutative Fusion Algebras

A commutative fusion algebra is proved to be amenable if and only if the associated regular representation is bounded.

Geometric Mean of States and Transition Amplitudes

The transition amplitude between square roots of states, which is an analogue of Hellinger integral in classical measure theory, is investigated in connection with operator-algebraic representation theory. A variational expression based on geometric mean of positive forms is utilized to obtain an approximation formula for transition amplitudes.

On Primitive Ideal Spaces of C*-Algebras over Certain Locally Compact Groupoids

Let F be a locally compact Hausdorff second countable groupoid with a left Haar system {v x } x∈X in the sense of [9] (X = the unit space of Γ). By analogy with Fell’s algebraic bundles over groups, we define the notion of C*-algebras over F and, given a C*-algebra A over Γ, we can form a C*-algebra C*(Γ, A) as the completion of the cross sectional algebra of A. In this note, under some stringent assumptions on Γ, we present a concrete realization of the primitive ideal space of C*(Γ, A). This is a C*-version of [12].

GEOMETRY OF QUASI-FREE STATES OF CCR ALGEBRAS

Geometric positions of square roots of quasi-free states of CCR algebras are investigated together with an explicit formula for transition amplitudes among them.

Tannaka duals in semisimple tensor categories

Abstract Tannaka duals of finite-dimensional Hopf algebras inside semisimple tensor categories are used to construct orbifold tensor categories, which are shown to include the Tannaka dual of the dual Hopf algebras. The second orbifolds are then monoidally equivalent to the initial tensor categories in a canonical fashion.

GEOMETRY OF COHERENT STATES OF CCR ALGEBRAS

Geometric positions of square roots of coherent states of CCR algebras are investigated along with an explicit formula for transition amplitudes among them, which is a natural extension of our previous results on quasi-free states and will provide a new insight into the quasi-equivalence problem on coherent states.