On the structure of tame graded basic Hopf algebras II

Abstract

In continuation of the article [G.X. Liu, On the structure of tame basic Hopf algebras, J. Algebra 299 (2006) 841-853] we classify all radically graded basic Hopf algebras of tame type over an algebraically closed field of characteristic 0.

On quiver-theoretic description for quasitriangularity of Hopf algebras

“…As is well-known, quiver methods are very useful in constructing algebras and studying their representations. Very nice quiver settings for elementary and pointed Hopf algebras have been built in various works [10,15,11,30] and shown their advantage in classifying some interesting classes of Hopf algebras as well as their representations, see for instance [9,14,23,7,20,19,16] and other related works. To us, it seems sensible to ask: is it possible to describe Drinfeld's quasitriangularity of Hopf algebras via combinatorial properties of Hopf quivers introduced by Cibils and Rosso [11]?…”

Commutative Hopf structures over a loop

“…Naturally there is a strong desire to apply this handy quiver tool to other algebraic structures. Such idea for Hopf algebras appeared explicitly in [5,6,8,11] and was showed to be very effective in dealing with the structures of finite-dimensional pointed (or dually, basic) Hopf algebras when the characteristic of the base field is 0 [8,3,16,15,14,19].…”

Progress of Research on Weak Hopf Algebra

“…This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Intelligent Systems Research, volume 143 1 fundamental theorem for Hopf modules is generalized to Weak Hopf algebras[8].…”