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Toeplitz CAR flows are a class of $E_{0}$ -semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non-cocycle-conjugate $E_{0}$ -semigroups of type III. We also generalize the type III criterion for Toeplitz canonical anticommutation relation (CAR) flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always either of type I or type III.

We show that any faithful quasi-free actions of a finite group on the Cuntz algebra $\mathcal{; ; O}; ; _\infty$ are mutually conjugate, and that they are asymptotically representable.

We show that every sum system is divisible. Combined with B. V. R. Bhat and R. Srinivasan's result, this shows that every product system arising from a sum system (and every generalized CCR flow) is either of type I or type III. A necessarily and sufficient condition for such a product system to be of type I is obtained., 22 pages

We introduce a new construction of $E_0$-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of $C_0$-semigroups. We get a new necessary and sufficient condition for them to be of type III, when the associated sum system is of finite index. Using this criterion, we construct examples of type III $E_0$-semigroups, which can not be distinguished from $E_0$-semigroups of type I by the invariants introduced by Boris Tsirelson. Finally, by considering the local von Neumann algebras, and by associating a type III factor to a given type III $E_0$-semigroup, we show that there exist uncountably many type III $E_0$-semigroups in this family, which are mutually non-cocycle conjugate., Comment: 45 pages

A quadrilateral of factors is an irreducible inclusion of factors $N \subset M$ with intermediate subfactors $P$ and $Q$ such that $P$ and $Q$ generate $M$ and the intersection of $P$ and $Q$ is $N$. We investigate the structure of a non-commuting quadrilateral of factors with all the elementary inclusions $P\subset M$, $Q\subset M$, $N\subset P$, and $N\subset Q$ 2-supertransitive. In particular we classify such quadrilaterals with the indices of the elementary subfactors less than or equal to 4. We also compute the angles between $P$ and $Q$ for quadrilaterals coming from $\alpha$-induction and asymptotic inclusions., Comment: 80 pages, 147 figures, to appear in International Journal of Mathematics

We completely classify the KMS states for the gauge action on a $C^*$-algebra associated with a rational function $R$ introduced in our previous work. The gauge action has a phase transition at $\beta = \log \deg R$. We can recover the degree of $R$, the number of branched points, the number of exceptional points and the orbits of exceptional points from the structure of the KMS states. We also classify the KMS states for $C^*$-algebras associated with some self-similar sets, including the full tent map and the Sierpinski gasket by a similar method., Comment: 32 pages, LaTeX2e formated

We prove that for any non-trivial product-type action α of SU q (n) (0

Reappearance of HCV-RNA followed by exacerbation of biochemical parameters after combination therapy consisting of interferon and ribavirin is an obstacle to achieve sustained response and improve long-term prognosis. We hypothesed that ribavirin monotherapy after 6 months of combination therapy may improve sustained viral and biochemical responses, and conducted a prospective, randomized and controlled study. Thirty-eight patients with chronic hepatitis C treated with combination therapy for 6 months and had no detectable serum HCV-RNA were enrolled, and allocated into two arms. Group I (n=19) was continuously administered oral ribavirin for additional 6 months, and group II (n=19) was followed up without any further treatment. At the end of trial, HCV-RNA negativity was 11/19 (58%) in group I, and 6/19 (32%) in group II (p=0.191). Multivariant analysis demonstrated that ribavirin monotherapy was not a predictor for the eradication of HCV-RNA. In cases without sustained viral responses, serum ALT levels at baseline and the end of 48 weeks' trial were 54.6 and 44.4 in group I (p=0.237), and significant reduction with ribavirin monotherapy was not observed. In conclusion, ribavirin monotherapy following combination therapy fails to improve sustained viral response as well as biochemical response.

We extend the notion of the canonical extension of automorphisms of type III factors to the case of endomorphisms with finite statistical dimensions. Following the automorphism case, we introduce two notions for endomorphisms of type III factors: modular endomorphisms and Connes-Takesaki modules. Several applications to compact groups of automorphisms and subfactors of type III factors are given from the viewpoint of ergodic theory.

We prove that if a conditional expectation from a simple $C^*$-algebra onto its $C^*$-subalgebra satisfies the Pimsner-Popa inequality, there exists a quasi-basis. As an application, we establish the Galois correspondence for outer actions of finite groups (and more generally finite dimensional Kac algebras) on simple $C^*$-algebras. We also introduce the notion of sectors for stable simple $C^*$-algebras and purely infinite simple $C^*$-algebras in the Cuntz standard form, and discuss several applications, including their relationship to $K$-theory.

Let $M$ be a factor with separable predual and $G$ a compact group of automorphisms of $M$ whose action is minimal, i.e. $M^{G^\prime}\cap M = C$, where $M^G$ denotes the $G$-fixed point subalgebra. Then every intemediate von Neumann algebra $M^G\subset N\subset M$ has the form $N=M^H$ for some closed subgroup $H$ of $G$. An extension of this result to the case of actions of compact Kac algebras on factors is also presented. No assumptions are made on the existence of a normal conditional expectation onto $N$., Comment: Plain TeX. An appendix in AMS-TeX has been added on October 30, 1997

Using fusion rules of sectors as a working hypothesis, we construct endomorphisms of the Cuntz algebra\(\mathcal{O}_n \) whose images have finite Watatani indices. Quasi-free KMS states on\(\mathcal{O}_n \) appear in a natural way associated with the endomorphisms, and we determine the Murray-von Neumann-Connes types of their GNS representations.

We survey two applications of sector theory to classification of subfactors. 1. A proof is given to A. Ocneanu’s announcement on the non-existence of the paragroups corresponding to the Coxeter graphs Dodd and E 7. 2. Goldman’s type theorem for subfactors with the principal graph A 5 is obtained.

Upon electrophoresis of Con-A, LCA-A, LCA-B and LCA at pH8.6, minor anodic components, which had no affinity for lectin-reactive AFP, were found in some lectin preparations. Time-dependent increase in electrophoretic mobility, spreading of electrophoretic band and loss of affinity for AFP were observed particularly with E-PHA when the lectin was dissolved in buffer at pH8.6 and kept at 4°C. These changes of E-PHA and the formation of minor bands of other lectins were reduced by lowering the pH to 7.5 and minimized by the presence as low as 0.1mM each of MnCl2, CaCl2 and MgCl2. LCA preparations were relatively stable at pH8.6 without added divalent cations. Lot to lot variations in electrophoretic mobility and affinity for AFP were found with LCA-B. Heterogeneity of subunit composition was also present in some lectins. Subunit molecular weights for the common and major component for each lectin, determined in the present study, were 27, 500 for Con-A, 19, 500 for LCA-A and 30, 000 for E-PHA. Lectin-reactive AFP was suggested as a simple and sensitive measure for quality control of lectins. Conversely, those variabilities of lectins should be taken into account in lectin-affinity electrophoresis of glycoproteins.

Motivated by B. Tsirelson's construction of E 0 -semigroups of type III, we investigate a C 0 -semigroup acting on the space of square integrable functions of the half line whose difference from the shift semigroup is a Hilbert–Schmidt operator. We give a description of such semigroups in terms of analytic functions on the right-half plane and construct several examples.

We discuss some relationships between two different fields, a non-commutative version of the Poisson boundary theory of random walks and the infinite tensor product (ITP) actions of compact quantum groups on von Neumann algebras. In contrast to the ordinary compact group case, the ITP action of a compact quantum group on a factor may allow non-trivial relative commutant of the fixed point subalgebra. We give a probabilistic description of the relative commutant in terms of a non-commutative Markov operator. In particular, we show that the following three objects can be naturally identified in the case of the quantum group SU q (2): (1) the relative commutant of the fixed point algebra under the action, (2) the space of harmonic elements for some non-commutative Markov operator on the dual quantum group of SU q (2), and (3) the weak closure L ∞ ( T \ SU q (2)) of one of the Podles quantum spheres. In view of the ordinary Poisson boundary theory of random walks on discrete groups, it shows that symbolically the quantum homogeneous space T \ SU q (2) may be regarded as the “Poisson boundary” of a non-commutative random walk on the dual object of SU q (2). An analogy of the Poisson integral formula is also given.