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

Methods

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

Instances

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

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

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

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

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

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

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

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

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

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

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

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