کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4666285 | 1345395 | 2012 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The Weyl group of the Cuntz algebra
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The Weyl group of the Cuntz algebra On is investigated. This is (isomorphic to) the group of polynomial automorphisms λu of On, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries Si and their adjoints. A necessary and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism λu restricts to an automorphism of the canonical diagonal MASA. Some steps towards a general criterion for invertibility of λu on the whole of On are also taken. A condition for verifying invertibility of a certain subclass of polynomial endomorphisms is given. First examples of polynomial automorphisms of On not inner related to those induced by unitaries from the core UHF subalgebra are exhibited, for every nâ¥2. In particular, the image of the Weyl group in the outer automorphism group of On is strictly larger than the image of the restricted Weyl group analyzed in previous papers. Results about the action of the Weyl group on the spectrum of the diagonal are also included.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 231, Issue 6, 20 December 2012, Pages 3147-3161
Journal: Advances in Mathematics - Volume 231, Issue 6, 20 December 2012, Pages 3147-3161
نویسندگان
Roberto Conti, Jeong Hee Hong, Wojciech SzymaÅski,