Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

Morphism from FiniteRankFreeModule to CliffordAlgebra

Suppose you have a finite rank free module with a basis:

M = FiniteRankFreeModule(QQ, 4, name='M', start_index=1)
m = M.basis('m');

and a Clifford algebra

Q = QuadraticForm(QQ,-2*matrix.identity(4))    
V.<e1,e2,e3,e4> = CliffordAlgebra(Q)

Is there a way to implement the quantization map $q:T(M)\to V$ from the tensor algebra to the Clifford algebra? It should satisfy $q(1) = 1$, $q(m[i]) = e_i$ and $q(a \otimes b) = q(a)*q(b)$.