کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1894292 | 1044159 | 2009 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A noncommutative view on topology and order
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: A noncommutative view on topology and order A noncommutative view on topology and order](/preview/png/1894292.png)
چکیده انگلیسی
In this paper we put forward the definition of particular subsets on a unital C∗C∗-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order relation defined on the spectrum of the algebra, which satisfies a compatibility condition with the topology (complete separateness). We prove that this space/algebra correspondence is a dual equivalence of categories, which generalizes the Gelfand–Naimark duality. Thus we can expect that general isocones could serve to define a notion of “noncommutative ordered spaces”. We also explore some basic algebraic constructions involving isocones, and classify those which are defined in M2(C)M2(C).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 59, Issue 7, July 2009, Pages 861–875
Journal: Journal of Geometry and Physics - Volume 59, Issue 7, July 2009, Pages 861–875
نویسندگان
Fabien Besnard,