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B.5.0.7 Qsl2

Procedure from library ncalg.lib (see ncalg_lib).

Usage:
Qsl2([n]), n an optional integer

Purpose:
set up the U_q(sl_2) = V_q(sl_2) / Qideal via the ring V_q(sl_2) and the ideal 'Qideal' in it;
if n is specified, the quantum parameter q will be specialized at the n-th root of unity

Return:
ring (V_q(sl_2))

Note:
you have to activate this ring with the 'setring' command.
In order to create the U_q(sl_2) from the output, you have to call the command like 'qring Usl2q = Qideal;'

Example:
 
LIB "ncalg.lib";
def A = Qsl2(3);
setring A;
Qideal;
==> Qideal[1]=Ke*Kf-1
qring Usl2q = Qideal;
Usl2q;
==> //   characteristic : 0
==> //   1 parameter    : q 
==> //   minpoly        : (q^2+q+1)
==> //   number of vars : 4
==> //        block   1 : ordering dp
==> //                  : names    E F Ke Kf 
==> //        block   2 : ordering C
==> //   noncommutative relations:
==> //    FE=E*F+(2/3*q+1/3)*Ke+(-2/3*q-1/3)*Kf
==> //    KeE=(-q-1)*E*Ke
==> //    KfE=(q)*E*Kf
==> //    KeF=(q)*F*Ke
==> //    KfF=(-q-1)*F*Kf
==> // quotient ring from ideal
==> _[1]=Ke*Kf-1
sl, Qsl3, Qso3


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