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 Incoming links: Hopf algebra

Over a field with

q \neq = 0

and

q^{2} \neq = 1

, this Hopf algebra has generators

E, F, K, K^{- 1}

and relations

K E = q^{2} E K

K F = q^{- 2} F K

and

EF - FE = (K - K^{- 1}) / (q - q^{- 1})

. One comultiplication convention is

Δ E = E \otimes K + 1 \otimes E

Δ F = F \otimes 1 + K^{- 1} \otimes F

and

Δ K = K \otimes K

. Its counit takes

E, F

to zero and

K

to one. The antipode takes

E

- E K^{- 1}

F

- K F

and

K

K^{- 1}