Numeric.Algebra.Hopf

Documentation

class Bialgebra r h => HopfAlgebra r h where

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

Instances

(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k TrigBasis

Methods

antipode :: (TrigBasis -> k) -> TrigBasis -> k

(TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => HopfAlgebra r QuaternionBasis'

Methods

antipode :: (QuaternionBasis' -> r) -> QuaternionBasis' -> r

(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis

Methods

antipode :: (HyperBasis -> k) -> HyperBasis -> k

(InvolutiveSemiring k, Rng k) => HopfAlgebra k DualBasis'

Methods

antipode :: (DualBasis' -> k) -> DualBasis' -> k

(TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => HopfAlgebra r QuaternionBasis

Methods

antipode :: (QuaternionBasis -> r) -> QuaternionBasis -> r

(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis'

Methods

antipode :: (HyperBasis' -> k) -> HyperBasis' -> k

(InvolutiveSemiring k, Rng k) => HopfAlgebra k DualBasis

Methods

antipode :: (DualBasis -> k) -> DualBasis -> k

(InvolutiveSemiring k, Rng k) => HopfAlgebra k ComplexBasis

Methods

antipode :: (ComplexBasis -> k) -> ComplexBasis -> k

(HopfAlgebra r a, HopfAlgebra r b) => HopfAlgebra r (a, b)

Methods

antipode :: ((a, b) -> r) -> (a, b) -> r

(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c) => HopfAlgebra r (a, b, c)

Methods

antipode :: ((a, b, c) -> r) -> (a, b, c) -> r

(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d) => HopfAlgebra r (a, b, c, d)

Methods

antipode :: ((a, b, c, d) -> r) -> (a, b, c, d) -> r

(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d, HopfAlgebra r e) => HopfAlgebra r (a, b, c, d, e)

Methods

antipode :: ((a, b, c, d, e) -> r) -> (a, b, c, d, e) -> r