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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).

nLab > Latest Changes: Killing form

Bottom of Page

1 to 4 of 4

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 6th 2022

    Outlined how the Killing form is often normalised making algebra elements corresponding to long roots have length 2\sqrt{2}. Planning to give the explicit examples for all the simple compact real forms.

    diff, v9, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2022

    I wouldn’t think it’s sensible to say (from your addition here)

    an inner product (hence positive definite)

    For one, this is explicitly not what it says at inner product.

    diff, v10, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 7th 2022

    Added details of the basic inner products for the (compact forms of the) simple real Lie algebras, and a citation for them

    diff, v11, current

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 7th 2022

    Removed the offending clause “hence positive definite” into a more neutral position.

    diff, v11, current

1 to 4 of 4

  1.