ON HOPF ALGEBRAS GENERATED BY COALGEBRAS
Author
RAGOZZINE, CHARLES B
Year
1999
Advisor
FERRAR, JOSEPH C.
Abstract
The concept of a free Hopf algebra generated by a coalgebra was introduced by Takeuchi to provide an example of a Hopf algebra with a non-bijective antipode. In general, this free Hopf algebra is not generated as an algebra by the coalgebra because of the way the antipode is obtained. Some classical quantum groups, however, have the properties that they are generated as an algebra by a matric coalgebra and that the antipode acts invariantly on the generating coalgebra. This thesis is devoted to the study of such Hopf algebras.
RAGOZZINE, CHARLES B
Year
1999
Advisor
FERRAR, JOSEPH C.
Abstract
The concept of a free Hopf algebra generated by a coalgebra was introduced by Takeuchi to provide an example of a Hopf algebra with a non-bijective antipode. In general, this free Hopf algebra is not generated as an algebra by the coalgebra because of the way the antipode is obtained. Some classical quantum groups, however, have the properties that they are generated as an algebra by a matric coalgebra and that the antipode acts invariantly on the generating coalgebra. This thesis is devoted to the study of such Hopf algebras.