تقرير
Structure for Regular Inclusions. II: Cartan envelopes, pseudo-expectations and twists
| العنوان: | Structure for Regular Inclusions. II: Cartan envelopes, pseudo-expectations and twists |
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| المؤلفون: | Pitts, David R. |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, 46L05, 46L07, 22A22 |
| الوصف: | We introduce the notion of a Cartan envelope for a regular inclusion (C,D). When a Cartan envelope exists, it is the unique, minimal Cartan pair into which (C,D) regularly embeds. We prove a Cartan envelope exists if and only if (C,D) has the unique faithful pseudo-expectation property and also give a characterization of the Cartan envelope using the ideal intersection property. For any covering inclusion, we construct a Hausdorff twisted groupoid using appropriate linear functionals and we give a description of the Cartan envelope for (C,D) in terms of a twist whose unit space is a set of states on C constructed using the unique pseudo-expectation. For a regular MASA inclusion, this twist differs from the Weyl twist; in this setting, we show that the Weyl twist is Hausdorff precisely when there exists a conditional expectation of C onto D. We show that a regular inclusion with the unique pseudo-expectation property is a covering inclusion and give other consequences of the unique pseudo-expectation property. Comment: 47 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2006.00834 |
| رقم الأكسشن: | edsarx.2006.00834 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |