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 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 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 nforum 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 sheaves 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).

nLab > Latest Changes: symplectic groupoid

Bottom of Page

1 to 8 of 8

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2009

    created stub for symplectic groupoid, effectively just regording my blog entries on Eli Hawkins' program of geometric quantization of Poisson manifolds

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 3rd 2009
    added definition and basic properties to symplectic groupoid, also one more blog reference
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2013
    • (edited Feb 2nd 2013)

    Have expanded the definition-section and added References to symplectic groupoid.

    I thought for a while that nowhere in the literature is the observation that a symplectic groupoid really is a 2-plectic structure and that its prequantization really involves a prequantum 2-bundle.

    But now I found, to my relief, that this is essentially made explicit in

    • Camille Laurent-Gengoux, Ping Xu, Quantization of pre-quasi-symplectic groupoids and their Hamiltonian spaces in The Breadth of Symplectic and Poisson Geometry Progress in Mathematics, 2005, Volume 232, 423-454 (arXiv:math/0311154)
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 27th 2023

    have polished up some of the references.

    Can’t find any online trace of this one, anymore:

    • Alan Weinstein, Noncommutative geometry and geometric quantization, in P. Donato et al. (eds.) Symplectic geometry and Mathematical physics, Progr. Math 99 Birkhäuser (1991) 446-461

    diff, v29, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 27th 2023

    Added a DOI for Weinstein: doi.

    diff, v30, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 27th 2023

    But it’s dead, no?

    • CommentRowNumber7.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 27th 2023

    The DOI is clearly valid, since it redirects to the Springer website. It also has the correct bibliographic information associated to it.

    The very point of a DOI is that it remains valid even if the website itself is malfunctioning.

    In this case, the whole Progress in Mathematics series appears to have malfunctioning DOI links. Presumably this will be noticed and fixed soon by Springer.

    • CommentRowNumber8.
    • CommentAuthorDavidRoberts
    • CommentTimeNov 28th 2023

    @Dmitri this still works: https://www.springer.com/series/4848/books?page=33. As does this much newer volume: https://doi.org/10.1007/978-3-031-27234-9, but the older books don’t seem to work.

1 to 8 of 8

  1.