Thread: algebra isomorphism View Single Post
 Sci Advisor HW Helper PF Gold P: 4,768 Consider the complex numbers C as an algebra over the reals R. The author of the book I have in front of me (Dirac operators in Riemannian Geometry, p.13) writes $$\mathbb{C}\otimes_{\mathbb{R}}\mathbb{C}=\mathbb{C}\oplus\mathbb{C}$$ (as real algebras). Does anyone know what this canonical algebra isomorphism is??? Obviously, woz -->(w,z) is not even linear.