Cliffard algebra defined by relation: $x*y+y*x=g(x,y)1$, where g(x,y) is bilinear symmetric form. What does mean $g(x,y)1$, why it's not just $g(x,y)$, without the identity?
2026-03-25 11:02:26.1774436546
Definition of Clifford Algebra
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The bilinear form $g$ is real-valued. But $x*y+y*x$ should be an element of the Clifford algebra. Hence you multiply $g(x,y)$ by $1$, which sits in the Clifford algebra, so that $g(x,y)\cdot 1$ is an element of the Clifford algebra.