Inclusions of C*-algebras arising from fixed-point algebras
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We examine inclusions of C *-algebras of the form AH ⊆ A Ìr G, where G and H are groups acting on a unital simple C *-algebra A by outer automorphisms and H is finite. It follows from a theorem of Izumi that AH ⊆ A is C *-irreducible, in the sense that all intermediate C *-algebras are simple. We show that AH ⊆ A Ìr G is C *-irreducible for all G and H as above if and only if G and H have trivial intersection in the outer automorphisms of A, and we give a Galois type classification of all intermediate C *-algebras in the case when H is abelian and the two actions of G and H on A commute. We illustrate these results with examples of outer group actions on the irrational rotation C *-algebras. We exhibit, among other examples, C *-irreducible inclusions of AF-algebras that have intermediate C *-algebras that are not AF-algebras; in fact, the irrational rotation C *-algebra appears as an intermediate C *-algebra.
Original language | English |
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Journal | Groups, Geometry, and Dynamics |
Volume | 18 |
Issue number | 1 |
Pages (from-to) | 127-145 |
ISSN | 1661-7207 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:
© 2023 European Mathematical Society.
- crossed product, fixed-point algebra, irrational rotation algebra, Irreducible inclusion of C-algebras
Research areas
ID: 385838180