Documentation

class Mon m whereSource

Monoid

Methods

Instances

Mon LaurentMonomial
Mon [a]
Mon (Permutation Int)
Mon (NonComMonomial v)
Ord a => Mon (SymmetricAlgebra a)
Mon (TensorAlgebra a)

class Algebra k b whereSource

Vect k b is a k-algebra

Methods

unit :: k -> Vect k bSource

mult :: Vect k (Tensor b b) -> Vect k bSource

Instances

Num k => Algebra k ()
Num k => Algebra k LaurentMonomial
Num k => Algebra k M3
Num k => Algebra k Mat2
Num k => Algebra k HBasis
(Num k, Ord v) => Algebra k (GlexMonomial v)
Num k => Algebra k (Permutation Int)
(Num k, Ord v) => Algebra k (NonComMonomial v)
(Num k, Ord a) => Algebra k (ExteriorAlgebra a)
(Num k, Ord a) => Algebra k (SymmetricAlgebra a)
(Num k, Ord a) => Algebra k (TensorAlgebra a)
(Num k, Ord a) => Algebra k [a]
Algebra Q (SL2 ABCD)
(Num k, Ord a, Ord b, Algebra k a, Algebra k b) => Algebra k (Tensor a b)
Algebra (LaurentPoly Q) (SL2q String)
Algebra (LaurentPoly Q) (M2q String)
Algebra (LaurentPoly Q) (Aq02 String)
Algebra (LaurentPoly Q) (Aq20 String)

class Coalgebra k b whereSource

Vect k b is a k-coalgebra

Methods

counit :: Vect k b -> kSource

comult :: Vect k b -> Vect k (Tensor b b)Source

Instances

Num k => Coalgebra k ()
Num k => Coalgebra k Mat2'
Num k => Coalgebra k HBasis
(Num k, Ord m, Mon m) => Coalgebra k (MonoidCoalgebra m)
Num k => Coalgebra k (SetCoalgebra b)
Num k => Coalgebra k (Permutation Int)
Coalgebra Q (SL2 ABCD)
(Num k, Ord a, Ord b, Coalgebra k a, Coalgebra k b) => Coalgebra k (Tensor a b)
Coalgebra (LaurentPoly Q) (SL2q String)
Coalgebra (LaurentPoly Q) (M2q String)

class (Algebra k b, Coalgebra k b) => Bialgebra k b Source

A bialgebra is an algebra which is also a coalgebra, subject to some compatibility conditions

Instances

Num k => Bialgebra k (Permutation Int)
Bialgebra Q (SL2 ABCD)
Bialgebra (LaurentPoly Q) (SL2q String)
Bialgebra (LaurentPoly Q) (M2q String)

class Bialgebra k b => HopfAlgebra k b whereSource

Methods

antipode :: Vect k b -> Vect k bSource

Instances

Num k => HopfAlgebra k (Permutation Int)
HopfAlgebra Q (SL2 ABCD)
HopfAlgebra (LaurentPoly Q) (SL2q String)

type Trivial k = Vect k ()Source

unit' :: (Num k, Algebra k b) => Trivial k -> Vect k bSource

counit' :: (Num k, Coalgebra k b) => Vect k b -> Trivial kSource

newtype SetCoalgebra b Source

Constructors

SC b

Instances

Num k => Coalgebra k (SetCoalgebra b)
Eq b => Eq (SetCoalgebra b)
Ord b => Ord (SetCoalgebra b)
Show b => Show (SetCoalgebra b)

newtype MonoidCoalgebra m Source

Constructors

MC m

Instances

(Num k, Ord m, Mon m) => Coalgebra k (MonoidCoalgebra m)
Eq m => Eq (MonoidCoalgebra m)
Ord m => Ord (MonoidCoalgebra m)
Show m => Show (MonoidCoalgebra m)

class Algebra k a => Module k a m whereSource

Methods

action :: Vect k (Tensor a m) -> Vect k mSource

Instances

Algebra k a => Module k a a
Num k => Module k Mat2 EBasis
(Num k, Ord a, Ord u, Ord v, Bialgebra k a, Module k a u, Module k a v) => Module k a (Tensor u v)
Num k => Module k (Permutation Int) Int
(Num k, Ord a, Ord u, Ord v, Algebra k a, Module k a u, Module k a v) => Module k (Tensor a a) (Tensor u v)

class Coalgebra k c => Comodule k c n whereSource

Methods

coaction :: Vect k n -> Vect k (Tensor c n)Source

Instances

Coalgebra k c => Comodule k c c
(Num k, Ord a, Ord m, Ord n, Bialgebra k a, Comodule k a m, Comodule k a n) => Comodule k a (Tensor m n)
Comodule (LaurentPoly Q) (M2q String) (Aq20 String)