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7.3.6 envelope

Syntax:
envelope ( ring_name )
Type:
ring
Purpose:
creates an enveloping algebra of a given algebra, that is $A^{env} = A \otimes_K A^{opp}$, where $A^{opp}$ is the opposite algebra of $A$.
Remark:
You have to activate the ring with the setring command. For the presentation, see explanation of opposite in opposite.
 
LIB "ncalg.lib";
def A = makeUsl2();
setring A; A;
==> // coefficients: QQ
==> // number of vars : 3
==> //        block   1 : ordering dp
==> //                  : names    e f h
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    fe=ef-h
==> //    he=eh+2e
==> //    hf=fh-2f
def Aenv = envelope(A);
setring Aenv;
Aenv;
==> // coefficients: QQ
==> // number of vars : 6
==> //        block   1 : ordering dp
==> //                  : names    e f h
==> //        block   2 : ordering a
==> //                  : names    H F E
==> //                  : weights  1 1 1
==> //        block   3 : ordering ls
==> //                  : names    H F E
==> //        block   4 : ordering C
==> // noncommutative relations:
==> //    fe=ef-h
==> //    he=eh+2e
==> //    hf=fh-2f
==> //    FH=HF-2F
==> //    EH=HE+2E
==> //    EF=FE-H
See oppose; opposite.