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B.5.0.1 sl

Procedure from library ncalg.lib (see ncalg_lib).

Usage:
sl(n,[p]); n an integer, n>1; p an optional integer (field characteristic)

Purpose:
set up the U(sl_n) in x(i),y(i),h(i) presentation over the field of char p

Return:
ring, describing

Note:
You have to activate this ring with the 'setring' command.
The presentation of U(sl_n) is derived from the standard presentation of sl_n,
where positive resp. negative roots are denoted by x(i) resp. y(i) and
Cartan elements are denoted by h(i).

Example:
 
LIB "ncalg.lib";
def a=sl(3);
setring a;
a;
==> //   characteristic : 0
==> //   number of vars : 8
==> //        block   1 : ordering dp
==> //                  : names    x(1) x(2) x(3) y(1) y(2) y(3) h(1) h(2) 
==> //        block   2 : ordering C
==> //   noncommutative relations:
==> //    x(2)x(1)=x(1)*x(2)-x(3)
==> //    y(1)x(1)=x(1)*y(1)-h(1)
==> //    y(3)x(1)=x(1)*y(3)+y(2)
==> //    h(1)x(1)=x(1)*h(1)+2*x(1)
==> //    h(2)x(1)=x(1)*h(2)-x(1)
==> //    y(2)x(2)=x(2)*y(2)-h(2)
==> //    y(3)x(2)=x(2)*y(3)-y(1)
==> //    h(1)x(2)=x(2)*h(1)-x(2)
==> //    h(2)x(2)=x(2)*h(2)+2*x(2)
==> //    y(1)x(3)=x(3)*y(1)+x(2)
==> //    y(2)x(3)=x(3)*y(2)-x(1)
==> //    y(3)x(3)=x(3)*y(3)-h(1)-h(2)
==> //    h(1)x(3)=x(3)*h(1)+x(3)
==> //    h(2)x(3)=x(3)*h(2)+x(3)
==> //    y(2)y(1)=y(1)*y(2)+y(3)
==> //    h(1)y(1)=y(1)*h(1)-2*y(1)
==> //    h(2)y(1)=y(1)*h(2)+y(1)
==> //    h(1)y(2)=y(2)*h(1)+y(2)
==> //    h(2)y(2)=y(2)*h(2)-2*y(2)
==> //    h(1)y(3)=y(3)*h(1)-y(3)
==> //    h(2)y(3)=y(3)*h(2)-y(3)
sl2, g2, gl, Qsl3, Qso3


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