Let $(E,g)$ be a vector space with a symmetric bilinear form, and $a,b$ be two endomorphisms of $E$. The generalized Clifford algebra is defined by the free algebra of $E$ with quotient by the relations: $$ a(e). b(f)+a(f).b(e)=(-g(a(e),b(f))-g(a(f),b(e)))1$$ with $e,f$ in $E$. Can I find a generalized spinors space over a "spin" manifold $M$? Can I have a Dirac operator (with $b=1$)?
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