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ClassSum ​

The -th class sum: add up one conjugacy class. Class sums are the basis of the CENTRE of — a commutative subalgebra of a usually non-commutative algebra.

WikipediaConjugacy classConjugacy classMathWorldConjugacyClassWikidataQ1353233nLabconjugacy class
ClassSum(group, k)the sum of the -th conjugacy class (1-indexed)
IsCentral(group, element)whether an element commutes with everything

Domain: Group algebras

Details
  • A single non-central element is not central, but the class sum containing it always is — that is the point
  • Class sums have disjoint supports, so they are linearly independent and form a basis of the centre
  • The first class is always the identity alone
  • is the number of conjugacy classes, which is also the number of irreducible characters of

Examples

See also: ConjugacyClasses, GroupBasis