The BV-algebra of a Jacobi manifold
نویسنده
چکیده
We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give a new example of a Lie bialgebroid on Poisson manifolds.
منابع مشابه
A Holomorphic Representation of the Jacobi Algebra
A representation of the Jacobi algebra h1 ⋊ su(1, 1) by first order differential operators with polynomial coefficients on the manifold C×D1 is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.
متن کاملA Holomorphic Representation of the Multidimensional Jacobi Algebra
A holomorphic representation of the Jacobi algebra hn⋊sp(n,R) by first order differential operators with polynomial coefficients on the manifold C × Dn is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.
متن کاملIsomorphisms of the Jacobi and Poisson Brackets
We present a general theorem describing the isomorphisms of the local Lie algebra structures on the spaces of smooth (real-analytic or holomorphic) functions on smooth (resp. real-analytic, Stein) manifolds, as for example those given by Poisson or contact structures, but we consider degenerate structures as well. Introduction We shall admit different classes of smoothness, so by a manifold of ...
متن کاملClosed String Field Theory: Quantum Action and the B-v Master Equation
The complete quantum theory of covariant closed strings is constructed in detail. The nonpolynomial action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra L∞ encoding the gauge symmetry of the classical theory. The higher genus...
متن کاملLocal Lie Algebra Determines Base Manifold *
It is proven that a local Lie algebra in the sense of A. A. Kirillov determines the base manifold up to a diffeomorphism provided the anchor map is nowhere-vanishing. In particular, the Lie algebras of nowhere-vanishing Poisson or Jacobi brackets determine manifolds. This result has been proven for different types of differentiability: smooth, real-analytic, and holomorphic. MSC 2000: Primary 1...
متن کامل