Talk:Lie superalgebra

Error in the article

The picture representing the graded Jacobi identity (in the last section of the article) is wrong. More precisely $\sigma ^{2}$ hasn't been drown correctly. 83.87.165.29 (talk) 01:57, 6 November 2008 (UTC)

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I cannot understand the classification part

The sections about classification need (I believe) to be seriously edited. Unfortunately I do not feel knowledgeable enough to do it myself, but here are the places which I find very unclear:

SU(m/n) These are the superunitary Lie algebras which have invariants:

$z.{\overline {z}}+iw.{\overline {w}}$

There is no mention of invariants anywhere before this place and I do not understand what kind of invariants are meant, how the indicated expression determines them and what do they have to do with classification of Lie superalgebras.

The objects are interchangeably referred to as algebras and groups. It confuses me a lot. Besides, supergroups are much more esoteric objects than superalgebras - the latter are just plain algebraic structures while the former require the notion of supermanifold, etc.

This happens all along the whole section. In the end, I cannot figure out what exactly are those superalgebras listed. According to the previous material, they should be described as pairs of vector spaces with appropriate bilinear operations between them. None of such structures are ever mentioned in the classification section. — Preceding unsigned comment added by 109.172.129.12 (talk) 17:59, 28 August 2018 (UTC)