Expand description
Finite-support Weyl algebras in canonical PBW form.
Given a finite free module with ordered basis z_0,...,z_(m-1) and an
alternating scalar-valued form omega, WeylAlgebra constructs
T(V) / (z_i z_j - z_j z_i - omega[i][j]).WeylAlgebra::standard is the usual rank-n algebra with generators
x_0,...,x_(n-1),d_0,...,d_(n-1) and relations
[d_i,x_j] = delta_ij. Elements are finite sparse sums in the PBW basis;
the algebra itself is infinite-dimensional. Positive characteristic is not
collapsed to the characteristic-zero differential-operator picture: the
larger center remains visible, and the polynomial action is documented as
non-faithful there.
This is a separate public pillar from crate::clifford. It shares the
commutative crate::scalar::Scalar coefficient discipline, but a Weyl
monomial needs an exponent vector rather than a finite blade mask.
Structs§
- Weyl
Algebra - A finite-support PBW Weyl algebra over
S. - Weyl
Element - A finite sparse sum of canonical PBW monomials.
- Weyl
Monomial - The exponent vector of one canonical PBW monomial
z_0^a_0 ... z_(m-1)^a_(m-1).
Enums§
- Weyl
Error - A checked failure while constructing or operating on a finite-support Weyl algebra.