Cosocle

In mathematics, the term cosocle has several related meanings.

In group theory, a cosocle of a group G, denoted by Cosoc(G), is the intersection of all maximal normal subgroups of G.[1]

If G is a quasisimple group, then Cosoc(G) = Z(G).[1]

In the context of Lie algebras, a cosocle of a symmetric Lie algebra is the eigenspace of its structural automorphism which corresponds to the eigenvalue +1. (A symmetric Lie algebra decomposes into the direct sum of its socle and cosocle.)[2]

See also

References

  1. 1 2 Adolfo Ballester-Bolinches, Luis M. Ezquerro, Classes of Finite Groups, 2006, ISBN 1402047185, p. 97
  2. ↑ Mikhail Postnikov, Geometry VI: Riemannian Geometry, 2001, ISBN 3540411089,p. 98


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