Mathematics – Quantum Algebra
Scientific paper
1999-09-14
Annales de l'Institut Fourier 52 (2002), 809-834
Mathematics
Quantum Algebra
19 pages, AMS-TeX file. The paper has been entirely re-written: in particular, we add a discussion of the possible generalisat
Scientific paper
The "quantum duality principle" states that the quantization of a Lie bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a quantization of the dual Lie bialgebra (through its associated formal Poisson group) - via a quantum formal series Hopf algebra (QFSHA) - and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more precisely, there exist functors QUEA --> QFSHA and QFSHA --> QUEA, inverse of each other, such that in either case the Lie bialgebra associated to the target object is the dual of that of the source object. Such a result was claimed true by Drinfeld, but seems to be unproved in literature: we give here a complete detailed proof of it.
No associations
LandOfFree
The quantum duality principle 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 The quantum duality principle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The quantum duality principle will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-656338