Path subcoalgebras, finiteness properties and quantum groups

Details Path subcoalgebras, finiteness properties and quantum groups Path subcoalgebras, finiteness properties and quantum groups

2010-12-20

arxiv.org/abs/1012.4335v2

Mathematics

Quantum Algebra

26p, new version

Scientific paper

We study subcoalgebras of path coalgebras that are spanned by paths (called path subcoalgebras) and subcoalgebras of incidence coalgebras, and propose a unifying approach for these classes. We discuss the left quasi-co-Frobenius and the left co-Frobenius properties for these coalgebras. We classify the left co-Frobenius path subcoalgebras, showing that they are direct sums of certain path subcoalgebras arising from the infinite line quiver or from cyclic quivers. We also discuss the coreflexive property for the considered classes of coalgebras. Finally, we investigate which of the co-Frobenius path subcoalgebras can be endowed with Hopf algebra structures, in order to produce some quantum groups with non-zero integrals, and classify all these structures over a field with primitive roots of unity of any order. These turn out to be liftings of quantum lines over certain not necessarily abelian groups.

Affiliated with

Also associated with

No associations

Rating

Path subcoalgebras, finiteness properties and quantum groups 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 Path subcoalgebras, finiteness properties and quantum groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Path subcoalgebras, finiteness properties and quantum groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-454109