Weak Projections onto a Braided Hopf Algebra

Mathematics – Quantum Algebra

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

10.1016/j.jalgebra.2007.04.009

We show that, under some mild conditions, a bialgebra in an abelian and coabelian braided monoidal category has a weak projection onto a formally smooth (as a coalgebra) sub-bialgebra with antipode; see Theorem 1.12. In the second part of the paper we prove that bialgebras with weak projections are cross product bialgebras; see Theorem 2.12. In the particular case when the bialgebra $A$ is cocommutative and a certain cocycle associated to the weak projection is trivial we prove that $A$ is a double cross product, or biproduct in Madjid's terminology. The last result is based on a universal property of double cross products which, by Theorem 2.15, works in braided monoidal categories. We also investigate the situation when the right action of the associated matched pair is trivial.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Weak Projections onto a Braided Hopf Algebra 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 Projections onto a Braided Hopf Algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak Projections onto a Braided Hopf Algebra will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-343370

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.