Here Hopf algebras play a dual role: first the (left) invariant differ- ential operators on an algebraic group form a cocommutative Hopf algebra, which coincides
M
tween Hopf algebras and Lie groups (or algebraic groups) We emphasize ential operators on an algebraic group form a cocommutative Hopf algebra,
Cartier IHES
In particular, in the last part of the course I gave a complete proof from scratch of Zhou's theorem (1994): Any finite- dimensional Hopf algebra over the complex
Schn
The second is cen- tered around those aspects of algebraic topology that played an important role in the development of Hopf algebra theory We organized our
historia hopf final
In order to include a character theory for infinite dimensional Hopf algebras, we must consider characters as elements of the Hopf algebra which are associated
Let A be a connected Hopf algebra of finite type over a field k Then it is proved in Andre [I] that A* = UL, the universal enveloping algebra of a Lie algebra L, if
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.
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
On the Structure of Hopf Algebras