The Grothendieck algebras of certain smash product semisimple Hopf algebras

Let H be a semisimple Hopf algebra over an algebraically closed field of positive characteristic p. Under the conditions that >dim ()(1/2) and inverted iota 2dim(), we determine all non-isomorphic irreducible representations of the smash product semisimple Hopf algebra #, where G is a cyclic group of order :=2dim(). We endow the Grothendieck algebra (G(()),*) of H with a new multiplication star and show that the Grothendieck algebra (G(#),*) of # is isomorphic to (G(),*)circle plus(/2)circle plus(G(),star)circle plus 2 as algebras. This reveals a relationship between the Grothendieck algebra of # and that of H.