Hopf Algebras of Dimension p

Hopf Algebras of Dimension

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integers n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd primes p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some pro...

HOPF ALGEBRAS OF DIMENSION 2 p 3 Proof

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integer n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd prime p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some progr...

FURTHER RESULTS ON SEMISIMPLE HOPF ALGEBRAS OF DIMENSION pq

Let p, q be distinct prime numbers, and k an algebraically closed field of characteristic 0. Under certain restrictions on p, q, we discuss the structure of semisimple Hopf algebras of dimension pq. As an application, we obtain the structure theorems for semisimple Hopf algebras of dimension 9q over k. As a byproduct, we also prove that odd-dimensional semisimple Hopf algebras of dimension less...

On the Coderivations of Some Hopf Algebras

Hopf Algebras of Dimension 14

Let H be a finite dimensional non-semisimple Hopf algebra over an algebraically closed field k of characteristic 0. If H has no nontrivial skew-primitive elements, we find some bounds for the dimension of H 1 , the second term in the coradical filtration of H. Using these results, we are able to show that every Hopf algebra of dimension 14 is semisimple and thus isomorphic to a group algebra or...

Generalized Path Algebras and Pointed Hopf Algebras

Most of pointed Hopf algebras of dimension p with large coradical are shown to be generalized path algebras. By the theory of generalized path algebras it is obtained that the representations, homological dimensions and radicals of these Hopf algebras. The relations between the radicals of path algebras and connectivity of directed graphs are given. 2000 Mathematics subject Classification: 16w3...