dorsal/arxiv
View SchemaPoincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups
| Authors | G. E. Arutuynov, A. P. Isaev, Z. Popowicz |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9502002 |
| URL | https://arxiv.org/abs/q-alg/9502002 |
| DOI | 10.1088/0305-4470/28/15/015 |
| Journal | J.Phys.A28:4349-4359,1995 |
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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"abstract": "We investigate the possibility to construct bicovariant differential calculi\non quantum groups SO_q(N) and Sp_q(N) as a quantization of an underlying\nbicovariant bracket.We show that, opposite to GL(N) and SL(N)-cases, neither of\npossible graded SO- and Sp- bicovariant brackets (associated with a\nquasitriangular r-matrices) obey the Jacobi identity when the differential\nforms are Lie algebra- valued. The absence of a classical Poisson structure\ngives an indication that differential algebras describing bicovariant\ndifferential calculi on quantum orthogonal and symplectic groups are not of\nPoincar\u0027e- Birkhoff- -Witt type.",
"arxiv_id": "q-alg/9502002",
"authors": [
"G. E. Arutuynov",
"A. P. Isaev",
"Z. Popowicz"
],
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"q-alg",
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],
"doi": "10.1088/0305-4470/28/15/015",
"journal_ref": "J.Phys.A28:4349-4359,1995",
"title": "Poincare\u0027-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups",
"url": "https://arxiv.org/abs/q-alg/9502002"
},
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