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7.5.16.0. quantMat
Procedure from library qmatrix.lib (see qmatrix_lib).
- Usage:
- quantMat(n [, p]); n integer (n>1), p an optional integer
- Return:
- ring (of quantum matrices). If p is specified, the quantum parameter q
will be specialized at the p-th root of unity
- Purpose:
- compute the quantum matrix ring of order n
- Note:
- activate this ring with the "setring" command.
The usual representation of the variables in this quantum
algebra is not used because double indexes are not allowed
in the variables. Instead the variables are listed by reading
the rows of the usual matrix representation, that is, there
will be n*n variables (one for each entry an n*N generic matrix),
listed row-wise
Example:
| | LIB "qmatrix.lib";
def r = quantMat(2); // generate O_q(M_2) at q generic
setring r; r;
==> // coefficients: QQ(q)
==> // number of vars : 4
==> // block 1 : ordering Dp
==> // : names y(1) y(2) y(3) y(4)
==> // block 2 : ordering C
==> // noncommutative relations:
==> // y(2)y(1)=1/(q)*y(1)*y(2)
==> // y(3)y(1)=1/(q)*y(1)*y(3)
==> // y(4)y(1)=y(1)*y(4)+(-q^2+1)/(q)*y(2)*y(3)
==> // y(4)y(2)=1/(q)*y(2)*y(4)
==> // y(4)y(3)=1/(q)*y(3)*y(4)
kill r;
def r = quantMat(2,5); // generate O_q(M_2) at q^5=1
setring r; r;
==> // coefficients: QQ[q]/(q^4+q^3+q^2+q+1)
==> // number of vars : 4
==> // block 1 : ordering Dp
==> // : names y(1) y(2) y(3) y(4)
==> // block 2 : ordering C
==> // noncommutative relations:
==> // y(2)y(1)=(-q^3-q^2-q-1)*y(1)*y(2)
==> // y(3)y(1)=(-q^3-q^2-q-1)*y(1)*y(3)
==> // y(4)y(1)=y(1)*y(4)+(-q^3-q^2-2*q-1)*y(2)*y(3)
==> // y(4)y(2)=(-q^3-q^2-q-1)*y(2)*y(4)
==> // y(4)y(3)=(-q^3-q^2-q-1)*y(3)*y(4)
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See also:
qminor.
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