کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8966122 | 1646771 | 2019 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Homomorphisms between different quantum toroidal and affine Yangian algebras
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
This paper concerns the relation between the quantum toroidal algebras and the affine Yangians of sln, denoted by Uq1,q2,q3(n) and Yh1,h2,h3(n), respectively. Our motivation arises from the milestone work [11], where a similar relation between the quantum loop algebra Uq(Lg) and the Yangian Yh(g) has been established by constructing an isomorphism of C[[ħ]]-algebras Φ:UËexpâ¡(ħ)(Lg)â¶â¼YËħ(g) (with Ë standing for the appropriate completions). These two completions model the behavior of the algebras in the formal neighborhood of h=0. The same construction can be applied to the toroidal setting with qi=expâ¡(ħi) for i=1,2,3 (see [11], [22]). In the current paper, we are interested in the more general relation: q1=Ïmneh1/m,q2=eh2/m,q3=Ïmnâ1eh3/m, where m,nâ¥1 and Ïmn is an mn-th root of 1. Assuming Ïmnm is a primitive n-th root of unity, we construct a homomorphism Φm,nÏmn between the completions of the formal versions of Uq1,q2,q3(m) and Yh1/mn,h2/mn,h3/mn(mn).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 223, Issue 2, February 2019, Pages 867-899
Journal: Journal of Pure and Applied Algebra - Volume 223, Issue 2, February 2019, Pages 867-899
نویسندگان
Mikhail Bershtein, Alexander Tsymbaliuk,