algebra-4.3: Constructive abstract algebra

Numeric.Algebra.Hopf

Synopsis

# Documentation

class Bialgebra r h => HopfAlgebra r h where Source #

A HopfAlgebra algebra on a semiring, where the module is free.

When antipode . antipode = id and antipode is an antihomomorphism then we are an InvolutiveBialgebra with inv = antipode as well

Minimal complete definition

antipode

Methods

antipode :: (h -> r) -> h -> r Source #

Instances

 Source # Methodsantipode :: (ComplexBasis -> k) -> ComplexBasis -> k Source # Source # Methodsantipode :: (DualBasis -> k) -> DualBasis -> k Source # Source # Methodsantipode :: (HyperBasis' -> k) -> HyperBasis' -> k Source # Source # Methodsantipode :: (QuaternionBasis -> r) -> QuaternionBasis -> r Source # Source # Methodsantipode :: (DualBasis' -> k) -> DualBasis' -> k Source # Source # Methodsantipode :: (HyperBasis -> k) -> HyperBasis -> k Source # Source # Methodsantipode :: (QuaternionBasis' -> r) -> QuaternionBasis' -> r Source # Source # Methodsantipode :: (TrigBasis -> k) -> TrigBasis -> k Source # (HopfAlgebra r a, HopfAlgebra r b) => HopfAlgebra r (a, b) Source # Methodsantipode :: ((a, b) -> r) -> (a, b) -> r Source # (HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c) => HopfAlgebra r (a, b, c) Source # Methodsantipode :: ((a, b, c) -> r) -> (a, b, c) -> r Source # (HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d) => HopfAlgebra r (a, b, c, d) Source # Methodsantipode :: ((a, b, c, d) -> r) -> (a, b, c, d) -> r Source # (HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d, HopfAlgebra r e) => HopfAlgebra r (a, b, c, d, e) Source # Methodsantipode :: ((a, b, c, d, e) -> r) -> (a, b, c, d, e) -> r Source #