کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4668755 1346071 2015 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Pseudodifferential extensions and adiabatic deformation of smooth groupoid actions
ترجمه فارسی عنوان
ضمیمههای پراکنده و تغییر شکل آدیاباتیک از فعالیتهای گروهبندی صاف
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
The adiabatic groupoid Gad of a smooth groupoid G is a deformation relating G with its algebroid. In a previous work, we constructed a natural action of R on the C*-algebra of zero order pseudodifferential operators on G and identified the crossed product with a natural ideal J(G) of C⁎(Gad). In the present paper we show that C⁎(Gad) itself is a pseudodifferential extension of this crossed product in a sense introduced by Saad Baaj. Let us point out that we prove our results in a slightly more general situation: the smooth groupoid G is assumed to act on a C*-algebra A. We construct in this generalized setting the extension of order 0 pseudodifferential operators Ψ(A,G) of the associated crossed product A⋊G. We show that R acts naturally on Ψ(A,G) and identify the crossed product of A by the action of the adiabatic groupoid Gad with an extension of the crossed product Ψ(A,G)⋊R. Note that our construction of Ψ(A,G) unifies the ones of Connes (case A=C) and of Baaj (G is a Lie group).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 139, Issue 7, October 2015, Pages 750-776
نویسندگان
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