An isomorphism theorem for infinite reduced free products
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915790367752192 |
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| author | Hirshberg, Ilan Phillips, N. Christopher |
| author_facet | Hirshberg, Ilan Phillips, N. Christopher |
| contents | Let C be a separable unital C*-algebra, not isomorphic to the complex numbers, equipped with a faithful tracial state. Let A be a unital direct limit of one dimensional NCCW complexes, also equipped with a faithful tracial state. Suppose there is a unital trace preserving embedding of A in the Jiang-Su algebra which is an isomorphism on K-theory. (For example, A could be C([0,1]) with Lebesgue measure, or the Jiang-Su algebra itself.) Let D be the infinite reduced free product of copies of C. Then the reduced free product A*D is isomorphic to D. If D has real rank zero and C is exact, then in place of A we can use C(X) for any contractible compact metric space X and any faithful tracial state on C(X). An example consequence is that the reduced free product of infinitely many copies of C([0, 1]), with Lebesgue measure, is isomorphic to the reduced free product of infinitely many copies of the Jiang-Su algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10220 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An isomorphism theorem for infinite reduced free products Hirshberg, Ilan Phillips, N. Christopher Operator Algebras 46L09 Let C be a separable unital C*-algebra, not isomorphic to the complex numbers, equipped with a faithful tracial state. Let A be a unital direct limit of one dimensional NCCW complexes, also equipped with a faithful tracial state. Suppose there is a unital trace preserving embedding of A in the Jiang-Su algebra which is an isomorphism on K-theory. (For example, A could be C([0,1]) with Lebesgue measure, or the Jiang-Su algebra itself.) Let D be the infinite reduced free product of copies of C. Then the reduced free product A*D is isomorphic to D. If D has real rank zero and C is exact, then in place of A we can use C(X) for any contractible compact metric space X and any faithful tracial state on C(X). An example consequence is that the reduced free product of infinitely many copies of C([0, 1]), with Lebesgue measure, is isomorphic to the reduced free product of infinitely many copies of the Jiang-Su algebra. |
| title | An isomorphism theorem for infinite reduced free products |
| topic | Operator Algebras 46L09 |
| url | https://arxiv.org/abs/2602.10220 |