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Some of my colleagues work on CFT's and quantum groups and I hear them talk a lot about $\widehat{su(2)}_k$ algebras. According to them (and the general physics literature) these are what mathematicians would call affine Kac-Moody algebras.

However the defining relations of the $\widehat{su(2)}$ level $k$ algebras are rather those of what a mathematician would call the affine $su(2)$ algebras. To obtain a Kac-Moody algebra one needs to introduce an extra derivation.[$\ast$]

Is there a reason for this (apparent) problem with the nomenclature?

[$\ast$] Also see my other post https://math.stackexchange.com/q/3322944/

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  • $\begingroup$ Would Mathematics be a better home for this question? $\endgroup$
    – Qmechanic ♦
    Commented Oct 31, 2019 at 16:53
  • $\begingroup$ That's what I thought first too, but then I had the idea that the experts here would perhaps know better why the physics community adopted a different terminology. (And because the mathematicians didnt respond to my other question there) $\endgroup$
    – NDewolf
    Commented Oct 31, 2019 at 21:55

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