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Coproduct ​

The coproduct : takes one element to a sum of `HopfTensor` pairs. Deconcatenation for QSym; the multiplicative extension of splitting a part for NSym.

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Coproduct(element), as a sum of tensor pairs

Domain: Hopf algebras

Details
  • This is what makes these Hopf algebras rather than merely algebras — the product puts things together, the coproduct pulls them apart
  • The two are tied by the bialgebra axiom , checked across every pair of basis elements up to degree 3 in both algebras
  • Both coproducts are coassociative
  • Tensor pairs use `HopfTensor(left, right)`, NOT `CircleTimes` — that head is already the shared ordered product
  • Graded: the two halves' degrees sum to the degree of the input

Examples

See also: QSymM, Antipode, Counit