This research concerns the action of a Hopf algebra H on an algebra R. These actions generalize the more familiar actions of groups as automorphisms, of Lie algebras as derivations, and of coactions of groups which give group-graded algebras. The principal investigator will study crossed products; duality problems involving the action of a Hopf algebra; the structure of general pointed Hopf algebras; the generalized Lie structure of associative algebras, where this Lie structure means that the Lie bracket is taken in a category of comodules of a suitable bialgebra; and extensions of Hopf algebras in categories. This research is concerned with an algebraic object called a Hopf algebra. While the area is quite technical, Hopf algebras are becoming of increasing interest, even to non mathematicians. Hopf algebras are useful in the type of knot theory that is of interest to molecular chemists. Certain types of Hopf algebras are now referred to as quantum groups in recognition of their applications in physics. Hopf algebras are used to study differential operators and to make combinatorics more like calculus.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9500649
Program Officer
Lance W. Small
Project Start
Project End
Budget Start
1995-06-01
Budget End
1998-08-31
Support Year
Fiscal Year
1995
Total Cost
$160,834
Indirect Cost
Name
University of Southern California
Department
Type
DUNS #
City
Los Angeles
State
CA
Country
United States
Zip Code
90089