Quantum Doubles of Certain Rank Two Pointed Hopf Algebras

نویسنده

  • S. BURCIU
چکیده

A certain class of rank two pointed Hopf algebras is considered. The simple modules of their Drinfel’d double is described using Radford’s method [Rad03]. The socle of the tensor product of two such modules is computed and a formula similar to the one in [Che00] is obtained in some conditions. Cases when such a tensor product is completely irreducible are also given in the last section.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Factorization of Simple Modules for Certain Pointed Hopf Algebras

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 ...

متن کامل

A Class of Quantum Doubles Which Are Ribbon Algebras

Andruskiewitsch and Schneider classify a large class of pointed Hopf algebras with abelian coradical. The quantum double of each such Hopf algebra is investigated. The quantum doubles of a family of Hopf algebras from the above classification are ribbon Hopf algebras. Introduction Quasitriangular Hopf algebras have an universal R-matrix which is a solution of the Yang-Baxter equation and their ...

متن کامل

Quantum Doubles From A Class Of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf a...

متن کامل

Two-parameter Quantum Groups and Drinfel’d Doubles

We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gln and sln. We show that these quantum groups can be realized as Drinfel’d doubles of certain Hopf subalgebras with respect to Hopf pairings. Using the Hopf pairing, we construct a corresponding R-matrix. The quantum groups have a natural n-dimensional module V . The R-matrix enables...

متن کامل

2 00 8 Representations of Pointed Hopf Algebras and Their Drinfel ’ D Quantum Doubles

We study representations of nilpotent type nontrivial liftings of quantum linear spaces and their Drinfel’d quantum doubles. We construct a family of Vermatype modules in both cases and prove a parametrization theorem for simple modules. We compute the Loewy and socle series of Verma modules under a mild restriction on the datum of a lifting. We find bases and dimensions of simple modules.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008