Introduction E9F5FC

Questions FFFFC0

• View
• Edit
• History
• Print

Clifford algebras

Clifford Algebra Recursions

{$Cl_{p+2,q}\cong Cl_{q,p}\otimes Cl_{2,0}$}

{$Cl_{p,q+2}\cong Cl_{q,p}\otimes Cl_{0,2}$}

{$Cl_{p+1,q+1}\cong Cl_{q,p}\otimes Cl_{1,1}$}

Note that {$Cl_{2,0}\cong M_2(\mathbb{R})$} and {$Cl_{0,2}\cong \mathbb{H}$}

We can derive the first two isomorphisms from

{$Cl_{p+2,0}\cong Cl_{0,p}\otimes Cl_{2,0}$}

{$Cl_{0,q+2}\cong Cl_{q,0}\otimes Cl_{0,2}$}