This application can be generalized to polynomials in n variables, using the Exterior algebra of an n-dimensional vector space.
22.
In particular, the exterior derivative gives the exterior algebra of differential forms on a manifold the structure of a differential algebra.
23.
The infinitesimal differentials of single variable calculus become differential forms in multivariate calculus, and their manipulation is done with exterior algebra.
24.
Examples of this are the exterior algebra, the symmetric algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras.
25.
Stated like this, the dichotomy makes no reference to the metric " ? ", only to exterior algebra.
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An exterior algebra is an example of a graded-commutative ring that is not commutative in the non-graded sense.
27.
Quantum group ) of the exterior algebra, in the same way that the Weyl algebra is a quantization of the symmetric algebra.
28.
So we can apply the fact of exterior algebra that there is a unique linear form L on \ Lambda ^ 2 V that
29.
With an "'antipode "'defined on homogeneous elements by, the exterior algebra is furthermore a Hopf algebra.
30.
:: That exterior algebra thing is old, when I was very new to physics, as I've said before.
