Examples of graded connected Hopf algebras with basis¶
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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 \(\tau(x\otimes y) = y\otimes x\).
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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 \(\tau(x\otimes y) = y\otimes x\).