envelopingAlgebra -- Create the enveloping algebra

Synopsis

Usage:

Ae = envelopingAlgebra(A,x)
Inputs:
- A, an instance of the type NCRing,
- x, a symbol,
Outputs:
- Ae, an instance of the type NCRing,

Description

This function returns the enveloping algebra A ** Aop. The symbol argument is used to define the variables in Aop.

i1 : B = skewPolynomialRing(QQ,(-1)_QQ, {a,b,c})
--Calling Bergman for NCGB calculation.
Complete!

o1 = B

o1 : NCQuotientRing

i2 : envelopingAlgebra(B,v)
--Calling Bergman for NCGB calculation.
Complete!
--Calling Bergman for NCGB calculation.
Complete!
--Calling Bergman for NCGB calculation.
Complete!
--Calling Bergman for NCGB calculation.
Complete!

o2 = QQ{a, b, c, v , v , v } / {ba+ab, ca+ac, cb+bc, v v +v v , v v +v v , v v +v v , v a-av , v a-av , v a-av , v b-bv } + More...
                  0   1   2                           1 0  0 1   2 0  0 2   2 1  1 2   0    0   1    1   2    2   0    0

o2 : NCQuotientRing

Ways to use envelopingAlgebra :

envelopingAlgebra(NCRing,Symbol)

For the programmer

The object envelopingAlgebra is a method function.