Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra

Details Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra

1997-04-11

arxiv.org/abs/q-alg/9704011v1

Mathematics

Quantum Algebra

29 pages, AMSLATEX

Scientific paper

10.1007/s002200050311

We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical W-algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL(2). The nontrivial consistency conditions fix the choice of the classical r-matrix defining the Poisson-Lie structure on the loop group LSL(2), and this leads to a new elliptic classical r-matrix. The reduced Poisson algebra coincides with the deformation of the classical Virasoro algebra previously defined in q-alg/9505025. We also consider a discrete analogue of this Poisson algebra. In the second part (q-alg/9702016) the construction is generalized to the case of an arbitrary semisimple Lie algebra.

Affiliated with

Also associated with

No associations

Rating

Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro 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 Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-353060