کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658491 | 1633102 | 2014 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Algebraically determined semidirect products
ترجمه فارسی عنوان
محصولات مرسوم خطی تعریف شده به طور جبری
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
چکیده انگلیسی
Let G be a Polish (i.e., complete separable metric topological) group. Define G to be an algebraically determined Polish group if given any Polish group L and an algebraic isomorphism Ï:Lâ¦G, then Ï is a topological isomorphism. The purpose of this paper is to prove a general theorem that gives useful sufficient conditions for a semidirect product of two Polish groups to be algebraically determined. This general theorem will provide a flowchart or recipe for proving that some special semidirect products are algebraically determined. For example, it may be used to prove that the natural semidirect product HâG, where H is the additive group of a separable Hilbert space and G is a Polish group of unitaries on H acting transitively on the unit sphere with âIâG, is algebraically determined. An example of such a G is the unitary group of a separable irreducible Câ-algebra with identity on H. Not all nontrivial semidirect products of Polish groups are algebraically determined, for it is known that the Heisenberg group H3(R) is a semidirect product of the form R2âθR1 and is not an algebraically determined Polish group.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 175, 15 September 2014, Pages 43-48
Journal: Topology and its Applications - Volume 175, 15 September 2014, Pages 43-48
نویسندگان
We'am M. Al-Tameemi, Robert R. Kallman,