Math.QuantumAlgebra.QuantumPlane

A module defining the quantum plane and its symmetries

Documentation

qvar :: Monomial m => v -> Vect (LaurentPoly Q) (m v)

a :: Monomial m => Vect (LaurentPoly Q) (m [Char])

b :: Monomial m => Vect (LaurentPoly Q) (m [Char])

c :: Monomial m => Vect (LaurentPoly Q) (m [Char])

d :: Monomial m => Vect (LaurentPoly Q) (m [Char])

detq :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => Vect (LaurentPoly Q) (m [Char])

x :: Monomial m => Vect (LaurentPoly Q) (m [Char])

y :: Monomial m => Vect (LaurentPoly Q) (m [Char])

u :: Monomial m => Vect (LaurentPoly Q) (m [Char])

v :: Monomial m => Vect (LaurentPoly Q) (m [Char])

aq20 :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => [Vect (LaurentPoly Q) (m [Char])]

newtype Aq20 v

Constructors

Aq20 (NonComMonomial v)

Instances

Monomial Aq20

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (Aq20 v)

powers :: Eq v => Aq20 v -> [(v, Int)]

Eq v => Eq (Aq20 v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

(==) :: Aq20 v -> Aq20 v -> Bool

(/=) :: Aq20 v -> Aq20 v -> Bool

Ord v => Ord (Aq20 v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

compare :: Aq20 v -> Aq20 v -> Ordering

(<) :: Aq20 v -> Aq20 v -> Bool

(<=) :: Aq20 v -> Aq20 v -> Bool

(>) :: Aq20 v -> Aq20 v -> Bool

(>=) :: Aq20 v -> Aq20 v -> Bool

max :: Aq20 v -> Aq20 v -> Aq20 v

min :: Aq20 v -> Aq20 v -> Aq20 v

(Eq v, Show v) => Show (Aq20 v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

showsPrec :: Int -> Aq20 v -> ShowS

show :: Aq20 v -> String

showList :: [Aq20 v] -> ShowS

Algebra (LaurentPoly Q) (Aq20 String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq20 String)

mult :: Vect (LaurentPoly Q) (Tensor (Aq20 String) (Aq20 String)) -> Vect (LaurentPoly Q) (Aq20 String)

Comodule (LaurentPoly Q) (M2q String) (Aq20 String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

coaction :: Vect (LaurentPoly Q) (Aq20 String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (Aq20 String))

aq02 :: (Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m, Ord (m [Char])) => [Vect (LaurentPoly Q) (m [Char])]

newtype Aq02 v

Constructors

Aq02 (NonComMonomial v)

Instances

Monomial Aq02

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (Aq02 v)

powers :: Eq v => Aq02 v -> [(v, Int)]

Eq v => Eq (Aq02 v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

(==) :: Aq02 v -> Aq02 v -> Bool

(/=) :: Aq02 v -> Aq02 v -> Bool

Ord v => Ord (Aq02 v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

compare :: Aq02 v -> Aq02 v -> Ordering

(<) :: Aq02 v -> Aq02 v -> Bool

(<=) :: Aq02 v -> Aq02 v -> Bool

(>) :: Aq02 v -> Aq02 v -> Bool

(>=) :: Aq02 v -> Aq02 v -> Bool

max :: Aq02 v -> Aq02 v -> Aq02 v

min :: Aq02 v -> Aq02 v -> Aq02 v

(Eq v, Show v) => Show (Aq02 v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

showsPrec :: Int -> Aq02 v -> ShowS

show :: Aq02 v -> String

showList :: [Aq02 v] -> ShowS

Algebra (LaurentPoly Q) (Aq02 String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq02 String)

mult :: Vect (LaurentPoly Q) (Tensor (Aq02 String) (Aq02 String)) -> Vect (LaurentPoly Q) (Aq02 String)

m2q :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => [Vect (LaurentPoly Q) (m [Char])]

newtype M2q v

Constructors

M2q (NonComMonomial v)

Instances

Monomial M2q

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (M2q v)

powers :: Eq v => M2q v -> [(v, Int)]

Eq v => Eq (M2q v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

(==) :: M2q v -> M2q v -> Bool

(/=) :: M2q v -> M2q v -> Bool

Ord v => Ord (M2q v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

compare :: M2q v -> M2q v -> Ordering

(<) :: M2q v -> M2q v -> Bool

(<=) :: M2q v -> M2q v -> Bool

(>) :: M2q v -> M2q v -> Bool

(>=) :: M2q v -> M2q v -> Bool

max :: M2q v -> M2q v -> M2q v

min :: M2q v -> M2q v -> M2q v

(Eq v, Show v) => Show (M2q v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

showsPrec :: Int -> M2q v -> ShowS

show :: M2q v -> String

showList :: [M2q v] -> ShowS

Bialgebra (LaurentPoly Q) (M2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Coalgebra (LaurentPoly Q) (M2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

counit :: Vect (LaurentPoly Q) (M2q String) -> LaurentPoly Q

comult :: Vect (LaurentPoly Q) (M2q String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String))

Algebra (LaurentPoly Q) (M2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (M2q String)

mult :: Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String)) -> Vect (LaurentPoly Q) (M2q String)

Comodule (LaurentPoly Q) (M2q String) (Aq20 String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

coaction :: Vect (LaurentPoly Q) (Aq20 String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (Aq20 String))

sl2q :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => [Vect (LaurentPoly Q) (m [Char])]

newtype SL2q v

Constructors

SL2q (NonComMonomial v)

Instances

Monomial SL2q

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (SL2q v)

powers :: Eq v => SL2q v -> [(v, Int)]

Eq v => Eq (SL2q v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

(==) :: SL2q v -> SL2q v -> Bool

(/=) :: SL2q v -> SL2q v -> Bool

Ord v => Ord (SL2q v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

compare :: SL2q v -> SL2q v -> Ordering

(<) :: SL2q v -> SL2q v -> Bool

(<=) :: SL2q v -> SL2q v -> Bool

(>) :: SL2q v -> SL2q v -> Bool

(>=) :: SL2q v -> SL2q v -> Bool

max :: SL2q v -> SL2q v -> SL2q v

min :: SL2q v -> SL2q v -> SL2q v

(Eq v, Show v) => Show (SL2q v)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

showsPrec :: Int -> SL2q v -> ShowS

show :: SL2q v -> String

showList :: [SL2q v] -> ShowS

HopfAlgebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

antipode :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (SL2q String)

Bialgebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Coalgebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

counit :: Vect (LaurentPoly Q) (SL2q String) -> LaurentPoly Q

comult :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String))

Algebra (LaurentPoly Q) (SL2q String)

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (SL2q String)

mult :: Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String)) -> Vect (LaurentPoly Q) (SL2q String)

yb :: (Ord b, Show b, Algebra (Vect Q LaurentMonomial) b) => Vect (LaurentPoly Q) (b, b) -> Vect (LaurentPoly Q) (b, b)