An explicit formula for PBW quantization
Let k be a field of characteristic zero, g a k-Lie algebra, e : Sg → Ug the symmetrization map. The PBW quantization is the one parameter family of associative products: x *t y = ∑p=0∞ Bp(x, y) tp (t ∈ k) where Bp is the homogeneous component of degree -p of the map B: Sg ⊗k Sg → Sg, B(x, y) = e-1 (...
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todo:paper_00927872_v30_n4_p1705_Cortinas2023-10-03T14:55:14Z An explicit formula for PBW quantization Cortiñas, G. Let k be a field of characteristic zero, g a k-Lie algebra, e : Sg → Ug the symmetrization map. The PBW quantization is the one parameter family of associative products: x *t y = ∑p=0∞ Bp(x, y) tp (t ∈ k) where Bp is the homogeneous component of degree -p of the map B: Sg ⊗k Sg → Sg, B(x, y) = e-1 (exey). In this paper we give an explicit formula for B. As an application, we prove that for each p ≥ 0, Bp is a bidifferential operator of order ≤ p. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00927872_v30_n4_p1705_Cortinas |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
Let k be a field of characteristic zero, g a k-Lie algebra, e : Sg → Ug the symmetrization map. The PBW quantization is the one parameter family of associative products: x *t y = ∑p=0∞ Bp(x, y) tp (t ∈ k) where Bp is the homogeneous component of degree -p of the map B: Sg ⊗k Sg → Sg, B(x, y) = e-1 (exey). In this paper we give an explicit formula for B. As an application, we prove that for each p ≥ 0, Bp is a bidifferential operator of order ≤ p. |
| format |
JOUR |
| author |
Cortiñas, G. |
| spellingShingle |
Cortiñas, G. An explicit formula for PBW quantization |
| author_facet |
Cortiñas, G. |
| author_sort |
Cortiñas, G. |
| title |
An explicit formula for PBW quantization |
| title_short |
An explicit formula for PBW quantization |
| title_full |
An explicit formula for PBW quantization |
| title_fullStr |
An explicit formula for PBW quantization |
| title_full_unstemmed |
An explicit formula for PBW quantization |
| title_sort |
explicit formula for pbw quantization |
| url |
http://hdl.handle.net/20.500.12110/paper_00927872_v30_n4_p1705_Cortinas |
| work_keys_str_mv |
AT cortinasg anexplicitformulaforpbwquantization AT cortinasg explicitformulaforpbwquantization |
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1807321793670676480 |