✦ LIBER ✦

On Pointed Ribbon Hopf Algebras

✍ Scribed by Shlomo Gelaki

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 288 KB
Volume: 181
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0145

No coin nor oath required. For personal study only.

✦ Synopsis

In his paper, ''On Kauffman's knot Invariants Arising from Finite w x Dimensional Hopf Algebras'' R1 , Radford constructed two extensive families of pointed Hopf algebras. The first one, denoted by H , n, q, N, generalizes Sweedler's well known 4-dimensional noncommutative and noncocommutative Hopf algebra. The second one, denoted by U , is Ž N, , .

a family of finite dimensional pointed unimodular ribbon Hopf algebras constructed for the purpose of computing knots and 3-manifold invariants.

Ž . X This family generalizes the well known quantum group U sl where q is q 2

📜 SIMILAR VOLUMES

Pointed Hopf Algebras of Dimensionp3

✍ S Caenepeel; S Dăscălescu 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 165 KB

We give a structure theorem for pointed Hopf algebras of dimension p 3 , having coradical kC , where k is an algebraically closed field of characteristic zero. p Combining this with previous results, we obtain the complete classification of all pointed Hopf algebras of dimension p 3 .

Finite-Dimensional Simple-Pointed Hopf A

Finite-Dimensional Simple-Pointed Hopf Algebras

✍ David E Radford 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 201 KB

Some of the first examples of Hopf algebras described over a field k w x which are neither commutative nor cocommutative 13, 14 involve elements a and x which satisfy the relations ⌬ a s a m a, ⌬ x s x m a q 1 m x, and xa s qax Ž . Ž . for some q g k \_ 0. With the advent of quantum groups these re

Constructing Pointed Hopf Algebras by Or

Constructing Pointed Hopf Algebras by Ore Extensions

✍ M Beattie; S Dăscălescu; L Grünenfelder 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 233 KB

We present a general construction producing pointed co-Frobenius Hopf algebras and give some classification results for the examples obtained.

Pointed Hopf Algebras and Kaplansky's 10

Pointed Hopf Algebras and Kaplansky's 10th Conjecture

✍ Shlomo Gelaki 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 293 KB

Radford constructed two families of finite-dimensional pointed Hopf w x algebras over a field k R1, 5.1, and 5.2 . The first one, denoted by H , is a family of pointed Hopf algebras which contains a subfamily n, q, N, of self dual pointed Hopf algebras, denoted by H . This subfamily Ž N, , . w x gen

A Galois-Type Correspondence Theory for

A Galois-Type Correspondence Theory for Actions of Finite-Dimensional Pointed Hopf Algebras on Prime Algebras

✍ Sara Westreich 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 130 KB

Lifting of Quantum Linear Spaces and Poi

Lifting of Quantum Linear Spaces and Pointed Hopf Algebras of Orderp3

✍ N Andruskiewitsch; H.-J Schneider 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 337 KB

We propose the following principle to study pointed Hopf algebras, or more generally, Hopf algebras whose coradical is a Hopf subalgebra. Given such a Hopf algebra A, consider its coradical filtration and the associated graded coalgebra gr A. Then gr A is a graded Hopf algebra, since the coradical A