کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772740 | 1413383 | 2017 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the Yang-Baxter equation and left nilpotent left braces
ترجمه فارسی عنوان
بر روی معادله یانگ-باکستر و چپ بریده بریده نشده است
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
We study non-degenerate involutive set-theoretic solutions (X,r) of the Yang-Baxter equation, we call them solutions. We prove that the structure group G(X,r) of a finite non-trivial solution (X,r) cannot be an Engel group. It is known that the structure group G(X,r) of a finite multipermutation solution (X,r) is a poly-Z group, thus our result gives a rich source of examples of braided groups and left braces G(X,r) which are poly-Z groups but not Engel groups. We find an explicit relation between the multipermutation level of a left brace and the length of the radical chain A(n+1)=A(n)âA introduced by Rump. We also show that a finite solution of the Yang-Baxter equation can be embedded in a convenient way into a finite left brace, or equivalently into a finite involutive braided group.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 4, April 2017, Pages 751-756
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 4, April 2017, Pages 751-756
نویسندگان
Ferran Cedó, Tatiana Gateva-Ivanova, Agata Smoktunowicz,