کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4588468 1334185 2007 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Factorization of simple modules for certain pointed Hopf algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Factorization of simple modules for certain pointed Hopf algebras
چکیده انگلیسی

We study the representations of two types of pointed Hopf algebras: restricted two-parameter quantum groups, and the Drinfel'd doubles of rank one pointed Hopf algebras of nilpotent type. We study, in particular, under what conditions a simple module can be factored as the tensor product of a one-dimensional module with a module that is naturally a module for the quotient by central group-like elements. For restricted two-parameter quantum groups, given θ a primitive ℓth root of unity, the factorization of simple uθy,θz(sln)-modules is possible, if and only if gcd((y−z)n,ℓ)=1. For rank one pointed Hopf algebras, given the data D=(G,χ,a), the factorization of simple D(HD)-modules is possible if and only if |χ(a)| is odd and |χ(a)|=|a|=|χ|. Under this condition, the tensor product of two simple D(HD)-modules is completely reducible, if and only if the sum of their dimensions is less than or equal to |χ(a)|+1.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 318, Issue 2, 15 December 2007, Pages 957-980