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 limit 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 subobject 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
    • CommentTimeMar 1st 2012
    • (edited Mar 1st 2012)

    I have been expanding and polishing the entry Heisenberg group.

    This had existed in bad shape for quite a while, but now it’s maybe getting into better shape.

    I tried to spend some sentences on issues which I find are rarely highlighted appropriately in the literature. So there is discussion now of the fact that

    • there are different Lie groups for a given Heisenberg Lie algebra,

    • and the appearance of an β€œii” in [q,p]=i[q,p] = i may be all understood as not picking the simply conncted ones of these;

    I also added remarks on the relation to Poisson brackets, and symplectomorphisms.

    In this context: either I am dreaming, or there is a mistake in the Wikipedia entry Poisson bracket - Lie algebra.

    There it says that the Poisson bracket is the Lie algebra of the group of symplectomorphisms. But instead, it is the Lie algebra of a central extension of the group of Hamiltonian symplectomorphisms.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2023

    added pointer to:

    • Ernst Binz, Sonja Pods, The geometry of Heisenberg groups β€” With Applications in Signal Theory, Optics, Quantization, and Field Quantization, Mathematical Surveys and Monographs 151, American Mathematical Society (2008) [ams:surv-151]

    (here and elsewhere, such as at Heisenberg Lie algebra)

    diff, v17, current