Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups
q-alg
2011-07-19 v1 Quantum Algebra
Abstract
We investigate the possibility to construct bicovariant differential calculi on quantum groups SO_q(N) and Sp_q(N) as a quantization of an underlying bicovariant bracket.We show that, opposite to GL(N) and SL(N)-cases, neither of possible graded SO- and Sp- bicovariant brackets (associated with a quasitriangular r-matrices) obey the Jacobi identity when the differential forms are Lie algebra- valued. The absence of a classical Poisson structure gives an indication that differential algebras describing bicovariant differential calculi on quantum orthogonal and symplectic groups are not of Poincar'e- Birkhoff- -Witt type.
Keywords
Cite
@article{arxiv.q-alg/9502002,
title = {Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups},
author = {G. E. Arutuynov and A. P. Isaev and Z. Popowicz},
journal= {arXiv preprint arXiv:q-alg/9502002},
year = {2011}
}
Comments
12 pages,latex