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nLab > Latest Changes: Heisenberg Lie n-algebra

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  1.  
    • 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.

1 to 3 of 3

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