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I was reading a paragraph of a book (you can find it here) where the author seems to suggest that the Clifford algebras [itex]\mathcal{C}\ell_{2,4}(\mathbb{R})[/itex] and [itex]\mathcal{C}\ell_{4,2}(\mathbb{R})[/itex] are isomorphic. In particular, at the third line after Equation (10.190), when he talks about the algebra with signature (4,2), the authors says:

"The signature shows that this space is isomorphic to the conformal algebra of spacetime"

where by "conformal algebra of spacetime" he means the algebra with signature (2,4).

How did he manage to deduce just from the signatures of these two algebras that they are indeed isomorphic?

I am not convinced of this statement, and I am wondering if there is a quick way to prove it (that I am missing).

Thanks!

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# Isomorphism between Clifford algebras CL(4,2) and CL(2,4)

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