Weak Hopf Algebras I: Integral Theory and C^*-structure

Details Weak Hopf Algebras I: Integral Theory and C^*-structure Weak Hopf Algebras I: Integral Theory and C^*-structure

1998-05-26

arxiv.org/abs/math/9805116v3

Mathematics

Quantum Algebra

40 pages, LaTeX, to appear in J. Algebra

Scientific paper

We give an introduction to the theory of weak Hopf algebras proposed recently as a coassociative alternative of weak quasi-Hopf algebras. We follow an axiomatic approach keeping as close as possible to the "classical" theory of Hopf algebras. The emphasis is put on the new structure related to the presence of canonical subalgebras A^L and A^R in any weak Hopf algebra A that play the role of non-commutative numbers in many respects. A theory of integrals is developed in which we show how the algebraic properties of A, such as the Frobenius property, or semisimplicity, or innerness of the square of the antipode, are related to the existence of non-degenerate, normalized, or Haar integrals. In case of C^*-weak Hopf algebras we prove the existence of a unique Haar measure h in A and of a canonical grouplike element g in A implementing the square of the antipode and factorizing into left and right algebra elements. Further discussion of the C^*-case will be presented in Part II.

Affiliated with

Also associated with

No associations

Rating

Weak Hopf Algebras I: Integral Theory and C^*-structure does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weak Hopf Algebras I: Integral Theory and C^*-structure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak Hopf Algebras I: Integral Theory and C^*-structure will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-113846