Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2012
    • CommentRowNumber2.
    • CommentAuthorcrogers
    • CommentTimeAug 25th 2012
    Urs, I don't think I agree with the table of "extensions" you have in the related concepts section. For any n, the unextended structure is the Hamiltonian vector fields, not (n-1)-forms. When X is (n-1) connected, the "Poisson Lie n-algebra" is quasi-isomorphic to a Lie n-algebra of Baez-Crans type. Its underlying vector space has in degree 0 the Hamiltonian vector fields, and in degree (n-1) the real numbers R. The associated (n+1)-cocycle is given by the n-plectic form evaluated at a point. When n=1, this recovers the famous Kostant-Souriau central extension. I describe this in Section 9 of this paper:
    http://arxiv.org/abs/1009.2975
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2012

    Sure, thanks for catching this! I have fixed it now.