Representation of Clifford algebras

asked 2022-04-14 22:23:12 +0200

cav_rt gravatar image

updated 2022-04-15 06:07:16 +0200

Is there a way of defining a matrix representation of Clifford algebras in sage?

For example, $Cl(3)$ is isomorphic to $M(2,\mathbb{C})$. Such isomorphism can be implemented by $\rho(e_i) = \sigma_i$, where $\sigma_i$ are the Pauli matrices.

In general, I would like to define an isomorphism $\rho :Cl(V,Q) \to M(n,\mathbb{K})$ and go back and forward between elements of $Cl(V,Q)$ and $M(n,\mathbb{K})$.

Is it possible in sage? I didn't find any hint on the documentation.

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