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arXiv · q-alg/9502002

Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups

G. E. Arutuynov·A. P. Isaev·Z. Popowicz
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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.

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G. E. Arutuynov, A. P. Isaev, Z. Popowicz. 1995-02-01. Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups. https://doi.org/10.1088/0305-4470/28/15/015

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