کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896605 | 1630589 | 2018 | 32 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Stability of group relations under small Hilbert-Schmidt perturbations
ترجمه فارسی عنوان
پایداری روابط گروهی تحت اختلالات هیلبرت-اشمیت کوچک
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
If matrices almost satisfying a group relation are close to matrices exactly satisfying the relation, then we say that a group is matricially stable. Here “almost” and “close” are in terms of the Hilbert-Schmidt norm. Using tracial 2-norm on II1-factors we similarly define II1-factor stability for groups. Our main result is that all 1-relator groups with non-trivial center are II1-factor stable. Many of them are also matricially stable and RFD. For amenable groups we give a complete characterization of matricial stability in terms of the following approximation property for characters: each character must be a pointwise limit of traces of finite-dimensional representations. This allows us to prove matricial stability for the discrete Heisenberg group H3 and for all virtually abelian groups. For non-amenable groups the same approximation property is a necessary condition for being matricially stable. We study this approximation property and show that RF groups with character rigidity have it.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 275, Issue 4, 15 August 2018, Pages 761-792
Journal: Journal of Functional Analysis - Volume 275, Issue 4, 15 August 2018, Pages 761-792
نویسندگان
Don Hadwin, Tatiana Shulman,