Editing Lie superalgebra (section)

==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'''(2''m'' + 1, ''n''), '''HO(m, m)''' (''m'' ≥ 2), '''SHO'''(''m'', ''m'') (''m'' ≥ 3), '''KO'''(''m'', ''m'' + 1), '''SKO(m, m + 1; β)''' (''m'' ≥ 2), '''SHO'''&nbsp;~&nbsp;(2''m'', 2''m''), '''SKO'''&nbsp;~&nbsp;(2''m'' + 1, 2''m'' + 3) and the five exceptional algebras:

::'''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)×'''S'''U(2)×'''U'''(1) as their zero level algebra. Infinite-dimensional (affine) Lie superalgebras are important symmetries in [[superstring theory]]. Specifically, the Virasoro algebras with <math>\mathcal{N}</math> supersymmetries are <math>K(1, \mathcal{N})</math> which only have central extensions up to <math>\mathcal{N} = 4</math>.<ref>{{harvnb|Kac|2010}}</ref>