Related Structures

CoefficientRing(U) : AlgQUE -> Fld

This returns the ring of coefficients of the quantized enveloping algebra U.

RootDatum(U) : AlgQUE -> RootDtm

This returns the root datum corresponding to the quantized enveloping algebra U.

PositiveRootsPerm(U) : AlgQUE -> SeqEnum

Given a quantized universal enveloping algebra U with root datum R returns a sequence consisting of the integers between 1 and the number of positive roots of R. If the k-th element of this sequence is m, then the generator F_k of U is of weight -β_m, where β_m is the m-th positive root of R (as returned by PositiveRoots(R)). (For the definition of weight of an element of U see Section PBW-type Bases.) Furthermore, the generator E_k is of weight β_m.

> R:= RootDatum("D4");
> U:= QuantizedUEA(R);
> CoefficientRing(U);
Univariate rational function field over Rational Field
Variables: q
> RootDatum(U);
Adjoint root datum of type D4 
> PositiveRootsPerm(U);
[ 1, 5, 2, 8, 6, 3, 12, 11, 9, 10, 7, 4 ]