7.3.6 envelope

Syntax:

envelope ( ring_name )

Type:

ring

Purpose:

creates an enveloping algebra of a given algebra, that is , where is the opposite algebra of .

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