Displaying similar documents to “Quantization of canonical cones of algebraic curves”

Divergence operators and odd Poisson brackets

Yvette Kosmann-Schwarzbach, Juan Monterde (2002)

Annales de l’institut Fourier

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We define the divergence operators on a graded algebra, and we show that, given an odd Poisson bracket on the algebra, the operator that maps an element to the divergence of the hamiltonian derivation that it defines is a generator of the bracket. This is the “odd laplacian”, Δ , of Batalin-Vilkovisky quantization. We then study the generators of odd Poisson brackets on supermanifolds, where divergences of graded vector fields can be defined either in terms of berezinian volumes or of...

From Poisson algebras to Gerstenhaber algebras

Yvette Kosmann-Schwarzbach (1996)

Annales de l'institut Fourier

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Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie...

Quantization and Morita equivalence for constant Dirac structures on tori

Xiang Tang, Alan Weinstein (2004)

Annales de l’institut Fourier

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We define a C * -algebraic quantization of constant Dirac structures on tori and prove that O ( n , n | ℤ ) -equivalent structures have Morita equivalent quantizations. This completes and extends from the Poisson case a theorem of Rieffel and Schwarz.

Linear hamiltonian circle actions that generate minimal Hilbert bases

Ágúst Sverrir Egilsson (2000)

Annales de l'institut Fourier

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The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper...