Classification of crossed-product -algebras associated with characters on free groups

Author:
Hong Sheng Yin

Journal:
Trans. Amer. Math. Soc. **320** (1990), 105-143

MSC:
Primary 46L55; Secondary 46L80

DOI:
https://doi.org/10.1090/S0002-9947-1990-0962286-2

MathSciNet review:
962286

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the classification problem of crossed-product -algebras of the form , where is a discrete group, is a one-dimensional character of , and is the unique -automorphism of such that if is the left regular representation of , then , . When , the free group on generators, we have a complete classification of these crossed products up to -isomorphism which generalizes the classification of irrational and rational rotation -algebras. We show that these crossed products are determined by two -theoretic invariants, that these two invariants correspond to two orbit invariants of the characters under the natural -action, and that these two orbit invariants completely classify the characters up to automorphisms of . The classification of crossed products follows from these results.

We also consider the same problem for some other groups.

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DOI:
https://doi.org/10.1090/S0002-9947-1990-0962286-2

Article copyright:
© Copyright 1990
American Mathematical Society