Drinfeld-Hecke algebras over cocommutative algebras

Details Drinfeld-Hecke algebras over cocommutative algebras Drinfeld-Hecke algebras over cocommutative algebras

2007-05-15

arxiv.org/abs/0705.2067v1

Mathematics

Rings and Algebras

26 pages; LaTeX

Scientific paper

If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra Sym(V) with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have families of deformations that have been studied widely in the literature; examples include symplectic reflection algebras and infinitesimal Hecke algebras. We introduce a family of deformations of these smash product algebras for general A, and characterize the PBW property. We then characterize the Jacobi identity for "grouplike" algebras (that include group rings and the nilCoxeter algebra), and precisely identify the PBW deformations in the example where A is the nilCoxeter algebra. We end with the more prominent case - where A is a Hopf algebra. We show the equivalence of several versions of the "deformed" relations in the smash product, and identify the PBW deformations which are Hopf algebras as well.

Affiliated with

Also associated with

No associations

Rating

Drinfeld-Hecke algebras over cocommutative algebras 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 Drinfeld-Hecke algebras over cocommutative algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Drinfeld-Hecke algebras over cocommutative algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-622751