تقرير
Towards a Classification of Multi-Faced Independence: A Representation-Theoretic Approach
| العنوان: | Towards a Classification of Multi-Faced Independence: A Representation-Theoretic Approach |
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| المؤلفون: | Gerhold, Malte, Hasebe, Takahiro, Ulrich, Michael |
| المصدر: | J. Funct. Anal. 285 (2023), no. 3, Paper No. 109907 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, Mathematics - Operator Algebras, 46L53 (Primary), 60A05, 18M05, 46L54 (Secondary) |
| الوصف: | We attack the classification problem of multi-faced independences, the first non-trivial example being Voiculescu's bi-freeness. While the present paper does not achieve a complete classification, it formalizes the idea of lifting an operator on a pre-Hilbert space in a "universal" way to a larger product space, which is key for the construction of (old and new) examples. It will be shown how universal lifts can be used to construct very well-behaved (multi-faced) independences in general. Furthermore, we entirely classify universal lifts to the tensor product and to the free product of pre-Hilbert spaces. Our work brings to light surprising new examples of 2-faced independences. Most noteworthy, for many known 2-faced independences, we find that they admit continuous deformations within the class of 2-faced independences, showing in particular that, in contrast with the single faced case, this class is infinite (and even uncountable). Comment: This update corrects a technical error in the latex source file, which caused several passages not to display in the pdf |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jfa.2023.109907 |
| URL الوصول: | http://arxiv.org/abs/2111.07649 |
| رقم الأكسشن: | edsarx.2111.07649 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jfa.2023.109907 |
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