Examples of graded connected Hopf algebras with basis

sage.categories.examples.graded_connected_hopf_algebras_with_basis.Example

This class illustrates an implementation of a graded Hopf algebra with basis that has one primitive generator of degree 1 and basis elements indexed by non-negative integers.

This Hopf algebra example differs from what topologists refer to as a graded Hopf algebra because the twist operation in the tensor rule satisfies

\[(\mu \otimes \mu) \circ (id \otimes \tau \otimes id) \circ (\Delta \otimes \Delta) = \Delta \circ \mu\]

where \(\tau(x\otimes y) = y\otimes x\).

sage.categories.examples.graded_connected_hopf_algebras_with_basis.GradedConnectedCombinatorialHopfAlgebraWithPrimitiveGenerator

This class illustrates an implementation of a graded Hopf algebra with basis that has one primitive generator of degree 1 and basis elements indexed by non-negative integers.

This Hopf algebra example differs from what topologists refer to as a graded Hopf algebra because the twist operation in the tensor rule satisfies

\[(\mu \otimes \mu) \circ (id \otimes \tau \otimes id) \circ (\Delta \otimes \Delta) = \Delta \circ \mu\]

where \(\tau(x\otimes y) = y\otimes x\).