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Results tagged with dg.differential-geometry
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user 61197
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
15
votes
1
answer
932
views
Associativity of Kontsevich's star product up to second order
In Deformation quantization of Poisson manifolds, Kontsevich gives the quantization formula
$$f \star g = \sum_{n=0}^\infty \hbar^n \sum_{\Gamma \in G_n} w_\Gamma B_{\Gamma,\alpha}(f,g).$$
He gives …
- 832
6
votes
Accepted
Associativity of Kontsevich's star product up to second order
The answer is that the black underlined terms do not cancel.
Instead, they contribute an extra term which gives precisely the Jacobi identity (times $2/3$).
(The reason I missed this is that I prev …
- 832
2
votes
0
answers
179
views
Nonlinear Poisson brackets associated with nilpotent (matrix) Lie algebras?
With every finite-dimensional Lie algebra $\mathfrak{g}$ one can associate a linear Poisson bracket on $\mathfrak{g}^\ast$. With some more restrictions on $\mathfrak{g}$ and some extra ingredients, th …
- 832