On Two Proofs for the Existence and Uniqueness of Integrals for Finite-Dimensional Hopf Algebras

Details On Two Proofs for the Existence and Uniqueness of Integrals for Finite-Dimensional Hopf Algebras On Two Proofs for the Existence and Uniqueness of Integrals for Finite-Dimensional Hopf Algebras

1999-11-11

arxiv.org/abs/math/9911081v1

Mathematics

Quantum Algebra

25 pages with diagrams. kauffman@uic.edu http://math.uic.edu/~kauffman, radford@uic.edu http://math.uic.edu/~radford

Scientific paper

This paper has two purposes. The first is to explicate the diagrammatic approach to Hopf algebras due to Kuperberg, and to examine his proof of the existence and uniqueness of integrals in both the diagrammatic and purely algebraic contexts. The second purpose of the paper is to show that the theory of integrals for a finite dimensional Hopf algebra A can be deduced from ideas concerning the trace function on End(A). Connections between Kuperberg's work and the trace function should be of interest to those who study three manifold invariants in relation to Hopf algebras.

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