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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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00927872_v30_n4_p1705_Cortinas |
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| Sumario: | 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. |
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