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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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