基本弱Hopf代数和弱覆盖箭图(Basic weak Hopf algebra and weak covering quiver)

Abstract

We introduce a finite-dimensional basic and split weak Hopf algebra H over an algebraically closed field k with strongly graded Jacobson radical r. We obtain some structures of a finite-dimensional basic and split semilattice graded weak Hopf algebra,and observe that there exists a finite Clifford monoid S which is isomorphic to the set of all the isomorphism classes of 1-dimensional H-modules such that . We also introduce the notion of weak covering quiver whose path algebra admits a structure of semilattice graded weak Hopf algebra, and classify the path algebra corresponding to the weak covering quiver. Furthermore,we prove that,for a finite-dimensional basic semilattice graded weak Hopf algebra H over an algebraically closed field k with strongly graded radical,there exists a weak covering quiver Γ such that ， where the ideal I is generated by the paths of length l≥2.

Keywords

• weak hopf algebra
• weak covering quiver
• ramification data