4 citations · 14 across the 15 of their papers we have counts for
7 papers · 1 filter
Oriented Quantum Algebras and Coalgebras, Invariants of Oriented 1-1 Tangles, Knots and Links
Louis Kauffman, David E. Radford
In this paper we study oriented quantum coalgebras which are structures closely related to oriented quantum algebras. We study the relationship between oriented quantum coalgebras…
Complete reducibility theorems for modules over pointed Hopf algebras
Nicolás Andruskiewitsch, David Radford, Hans-Jürgen Schneider
We investigate the representation theory of a large class of pointed Hopf algebras, extending results of Lusztig and others. We classify all simple modules in a suitable category a…
Representations of pointed Hopf algebras and their Drinfel'd quantum doubles
Leonid Krop, David Radford
We study representations of nilpotent type nontrivial liftings of quantum linear spaces and their Drinfel'd quantum doubles. We construct a family of Verma- type modules in both ca…
Representations Parameterized by a Pair of Characters
David E. Radford, Hans-Jürgen Schneider
Let and be algebras over a field . We study algebra structures on the underlying tensor product of vector spaces which satisfy $(u{\otimes}a)(u'{\otime…
On the irreducible representations of a class of pointed Hopf algebras
David E. Radford, Hans-Jürgen Schneider
We parameterize the finite-dimensional irreducible representations of a class of pointed Hopf algebras over an algebraically closed field of characteristic zero by dominant charact…
Biproducts and Two-Cocycle Twists of Hopf Algebras
David E. Radford, Hans-Jürgen Schneider
Let be a Hopf algebra with bijective antipode over a field and suppose that $R{#}H$ is a bi-product. Then is a bialgebra in the Yetter--Drinfel'd category ${}_H^H{\math…
On Two Proofs for the Existence and Uniqueness of Integrals for Finite-Dimensional Hopf Algebras
Louis H. Kauffman, David E. Radford
This paper has two purposes. The first is to explicate the diagrammatic approach to Hopf algebras due to Kuperberg, and to examine his proof of the existence and uniqueness of inte…