On the Irreducible Representations of a Class of Pointed Hopf Algebras
نویسنده
چکیده
We parameterize the finite-dimensional irreducible representations of a class of pointed Hopf algebras over an algebraically closed field of characteristic zero by dominant characters. The Hopf algebras we are considering arise in the work of N. Andruskiewitsch and the second author. Special cases are the multiparameter deformations of the enveloping algebras of semisimple Lie algebras where the deforming parameters are not roots of unity and some of their finitedimensional versions in the root of unity case.
منابع مشابه
Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Nichols Type
The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Nichols type Hopf algebras. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras
متن کاملClassification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type One
The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras
متن کاملRepresentations Parameterized by a Pair of Characters
Let U and A be algebras over a field k. We study algebra structures H on the underlying tensor product U⊗A of vector spaces which satisfy (u⊗a)(u′⊗a′) = uu′⊗aa′ if a = 1 or u′ = 1. For a pair of characters ρ ∈ Alg(U, k) and χ ∈ Alg(A, k) we define a left H-module L(ρ, χ). Under reasonable hypotheses the correspondence (ρ, χ) 7→ L(ρ, χ) determines a bijection between character pairs and the isom...
متن کاملOn the Classification of Finite-dimensional Pointed Hopf Algebras
We classify finite-dimensional complex Hopf algebras A which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements G(A) is abelian such that all prime divisors of the order of G(A) are > 7. Since these Hopf algebras turn out to be deformations of a natural class of generalized small quantum groups, our result can be read as an axiom...
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کامل