Pointed Hopf Algebras and Kaplansky's 10th Conjecture

✍ Scribed by Shlomo Gelaki

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 293 KB
• Volume: 209
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7513

✦ Synopsis

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 generalizes Taft's well-known Hopf algebras G1, T . The second one, denoted by U , is a family of pointed, unimodular, and ribbon Hopf Ž N, , .

algebras constructed for the purpose of computing invariants of knots, links, and 3-manifolds. This family generalizes the well-known quantum Ž . group U sl Ј when q is a root of unity. The author constructed a new q 2 family of finite-dimensional Hopf algebras, denoted by H H , which n, q, N, , ␣ generalizes Radford's H , and furthermore proved that this new n, q, N,