On the Structure of Hopf Algebras. By JOHN W. MILNOR and JOHN C. MOORE*. The notion of Hopf algebra' has been abstracted from the work of Hopf.
Here Hopf algebras play a dual role: first the (left) invariant differ- ential operators on an algebraic group form a cocommutative Hopf algebra which
MULTIPLIER HOPF ALGEBRAS. A. VAN DAELE. ABSTRACT. In this paper we generalize the notion of Hopf algebra. We consider an algebra A with or without identity
FOR HOPF ALGEBRAS. By RICHARD GUSTAVUS LARSON * and Moss EISENBERG SWEEDLER. It is well-known that certain Hopf algebras contain non zero elements.
3 Algebras coalgebras
Kaplansky has conjec- tured [1]: A finite-dimensional cosemisimple Hopf algebra is involutory. In this paper we show that if the characteristic of the ground
dimensional Hopf algebras. The key step of our approach will be the following. THEOREM 2.8. Let A be a Hopf algebra of dimension _< 11 that is not.
Integrals for Hopf algebras*. By Moss EISENBERG SWEEDLER. Introduction. For a Hopf algebra which is the "coordinate" ring of a compact Lie group.
There are many examples of familiar combinatorial objects which can be given the structure of a. Hopf algebra we look at a few simple examples at the end of
A morphism of bialgebras f : A ? B is a linear map which is both an algebra and a coalgebra homomorphism. Page 4. 4. HOPF ALGEBRAS. 2.2. Test Lemmas. Lemma