ORE EXTENSIONS AS WEAK HOPF ALGEBRAS

We use a technique introduced by M. Beattie et al for constructing finite dimensional pointed Hopf algebras. We apply this technique to obtain the Ore extension of the algebra kS of a finite commutative Clifford monoid S. This Ore extension is a non-commutative and non-cocommutative pointed semilattice graded weak Hopf algebra. Its quotients are finite dimensional pointed semilattice graded weak Hopf algebras. Finally, we obtain the Ore extension of the algebra of the dual of the commutative Clifford monoid.