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
    • CommentTimeFeb 8th 2012
    • (edited Feb 8th 2012)

    I have half-heartedly started adding something to Kac-Moody algebra. Mostly refrences so far. But I don’t have the time right now to do any more.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeFeb 8th 2012
    • (edited Feb 8th 2012)

    I have created the related entry affine Lie algebra. I think Kac-Moody Lie algebra should focus on general theory and references and examples for nonaffine case. Affine case is the main case in (geometric and physical) applications and we will undoubtfully have much about it, so it deserves to have its own entry. However I see now that there is an overlap with the existing entry current algebra.

    BTW, I do not feel strongly about it, but I think that the general convention was that the default name is the full name, so tangent Lie algebroid rather than Lie algebroid, Hausdorff topological space rather than Hausdorff space and then I guess Kac-Moody Lie algebra rather than Kac-Moody algebra, though all those cases are usually correct to refer both ways.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2012

    Hi Zoran,

    yes, I fully agree. I had similar thoughts already. But didn’t find the leisure to implement them.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2012
    • (edited Feb 8th 2012)

    It may make sense to keep current algebra a separate entry from affine Kac-Moody Lie algebra, I suppose. The former term alludes more to the fact that one thinks of vertex operator algebras and CFT, while the latter is more the purely Lie algebraic concept. Roughly.

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeFeb 8th 2012

    Right, I am not completely sure (current algebra vs. affine Lie algebra), the flavour and literature is a bit separated and the terminology also changed from 1960s when current algebra could also mean classical and quantum (like with or without the central charge). But I am not an expert on this terminology. In any case, someone competent should decide how to explain the terminology and cross-link accordingly.

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 20th 2023

    Added higher Kac-Moody algebra as a related concept. Since this now clashes with

    The higher Kac-Moody analogs of the exceptional semisimple Lie algebras E7, E7, E8 are…

    I have rewritten as

    The sequence of exceptional semisimple Lie algebras E7, E7, E8 may be continued to the Kac-Moody algebras:

    diff, v13, current