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7.5.10.0. makeUgl
Procedure from library ncalg.lib (see ncalg_lib).
- Usage:
- makeUgl(n,[p]); n an int, n>1; p an optional int (field characteristic)
- Return:
- ring
- Purpose:
- set up the U(gl_n) in the (e_ij (1<i,j<n)) presentation (where e_ij corresponds to a matrix with 1 at i,j only) over the field of char p
- Note:
- activate this ring with the
setring command
the variables are ordered as e_12,e_13,...,e_1n,e_21,...,e_nn.
Example:
| | LIB "ncalg.lib";
def a=makeUgl(3);
setring a; a;
==> // coefficients: QQ
==> // number of vars : 9
==> // block 1 : ordering dp
==> // : names e_1_1 e_1_2 e_1_3 e_2_1 e_2_2 e_2_3 e_3_1 \
e_3_2 e_3_3
==> // block 2 : ordering C
==> // noncommutative relations:
==> // e_1_2e_1_1=e_1_1*e_1_2-e_1_2
==> // e_1_3e_1_1=e_1_1*e_1_3-e_1_3
==> // e_2_1e_1_1=e_1_1*e_2_1+e_2_1
==> // e_3_1e_1_1=e_1_1*e_3_1+e_3_1
==> // e_2_1e_1_2=e_1_2*e_2_1-e_1_1+e_2_2
==> // e_2_2e_1_2=e_1_2*e_2_2-e_1_2
==> // e_2_3e_1_2=e_1_2*e_2_3-e_1_3
==> // e_3_1e_1_2=e_1_2*e_3_1+e_3_2
==> // e_2_1e_1_3=e_1_3*e_2_1+e_2_3
==> // e_3_1e_1_3=e_1_3*e_3_1-e_1_1+e_3_3
==> // e_3_2e_1_3=e_1_3*e_3_2-e_1_2
==> // e_3_3e_1_3=e_1_3*e_3_3-e_1_3
==> // e_2_2e_2_1=e_2_1*e_2_2+e_2_1
==> // e_3_2e_2_1=e_2_1*e_3_2+e_3_1
==> // e_2_3e_2_2=e_2_2*e_2_3-e_2_3
==> // e_3_2e_2_2=e_2_2*e_3_2+e_3_2
==> // e_3_1e_2_3=e_2_3*e_3_1-e_2_1
==> // e_3_2e_2_3=e_2_3*e_3_2-e_2_2+e_3_3
==> // e_3_3e_2_3=e_2_3*e_3_3-e_2_3
==> // e_3_3e_3_1=e_3_1*e_3_3+e_3_1
==> // e_3_3e_3_2=e_3_2*e_3_3+e_3_2
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See also:
makeUg2;
makeUsl.
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