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7.5.10.0. makeQsl2
Procedure from library ncalg.lib (see ncalg_lib).
- Usage:
- makeQsl2([n]), n an optional int
- Return:
- ring
- Purpose:
- define the U_q(sl_2) as a factor-ring of a ring V_q(sl_2) modulo the ideal
Qideal
- Note:
- the output consists of a ring, presenting V_q(sl_2) together with the ideal called
Qideal in this ring
activate this ring with the setring command
in order to create the U_q(sl_2) from the output, execute the command like qring Usl2q = Qideal;
If n is specified, the quantum parameter q will be specialized at the n-th root of unity
Example:
| | LIB "ncalg.lib";
def A = makeQsl2(3);
setring A;
Qideal;
==> Qideal[1]=Ke*Kf-1
qring Usl2q = Qideal;
Usl2q;
==> // coefficients: QQ[q]/(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
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See also:
makeQsl3;
makeQso3;
makeUsl.
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