Journal of Operator Theory

Volume 50, Issue 1, Summer 2003 pp. 119-130.

Automorphisms of free product-type and their crossed-products

Authors: Fumio Hiai

$1$ and Yoshimichi Ueda

$2$
Author institution:

$1$ Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980--8579, Japan

$2$ Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739--8526, Japan; Current address: Graduate School of Mathematics, Kyushu University, Fukuoka, 810--8560, Japan

Summary: A continuous family of non-outer conjugate aperiodic automorphisms whose crossed-products are all isomorphic is given on every interpolated free group factor. An explicit ``duality" relationship between compact co-commutative Kac algebra

$minimal$ free product actions and free shift actions is also discussed.

Keywords: Free product, crossed-product, aperiodic automorphism, amalgamated free product, free shift, interpolated free group factor, free Araki-Woods factor

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