On Lie Algebras in the Category of Yetter-Drinfeld Modules

Details On Lie Algebras in the Category of Yetter-Drinfeld Modules On Lie Algebras in the Category of Yetter-Drinfeld Modules

1996-12-17

arxiv.org/abs/q-alg/9612023v1

Mathematics

Quantum Algebra

21 pages, NLaTeX with bezier.sty, amsart.sty

Scientific paper

The category of Yetter-Drinfeld modules over a Hopf algebra (with bijektive antipode over a field) is a braided monoidal category. Given a Hopf algebra in this category then the primitive elements of this Hopf algebra do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in the category of Yetter-Drinfeld modules such that the set of primitive elements of a Hopf algebra is a Lie algebra in this sense. It has n-ary partially defined Lie multiplications on certain symmetric submodules of n- fold tensor products. They satisfy antisymmetry and Jacobi identities. Also the Yetter-Drinfeld module of derivations of an associative algebra in the category of Yetter- Drinfeld modules is a Lie algebra. Furthermore for each Lie algebra in the category of Yetter-Drinfeld modules there is a universal enveloping algebra which turns out to be a (braided) Hopf algebra in this category.

Affiliated with

Also associated with

No associations

Rating

On Lie Algebras in the Category of Yetter-Drinfeld Modules 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 On Lie Algebras in the Category of Yetter-Drinfeld Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Lie Algebras in the Category of Yetter-Drinfeld Modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-522289