Classification of Infinite Dimensional Simple Linearly Compact Lie Superalgebras
The classification consists of the 10 series W(m, n), S(m, n) ((m, n) ≠ (1, 1)), H(2m, n), K(2m+1, n), HO(m,m) (m ≥ 2), SHO(m,m) (m ≥ 3), KO(m,m + 1), SKO(m,m + 1; β) (m ≥ 2), SHO∼(2m,2m), SKO∼(2m+1,2m + 3) and the 5 exceptional algebras:
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- E(1,6), E(5,10), E(4,4), E(3,6), E(3,8)
The last two are particularly interesting (according to Kac) because they have the standard model gauge group SU(3)xSU(2)xU(1) as their zero level algebra. Infinite dimensional (affine) Lie superalgebras are important symmetries in superstring theory.
Read more about this topic: Lie Superalgebra
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