ag.algebraic geometry - What is the 1D and 2D Gamma matrices satisfying the Clifford Algebra?

Your question seems to be to identify the Clifford algebras $Cl(0,1)$ and $Cl(0,2)$ in the usual mathematics notation of, say, Spin Geometry by Lawson and Michelsohn. It is very easy to show that

$$Cl(0,1) cong mathbb{R} oplus mathbb{R}$$
and
$$Cl(0,2) cong mathbb{R}(2),$$
where $mathbb{R}(2)$ is the algebra of $2times 2$ real matrices.

There are two inequivalent one-dimensional irreducible representations of $Cl(0,1)$, where the gamma matrix (here a real number) is $Gamma^1=pm 1$.

There is a unique two-dimensional irreducible representation of $Cl(0,2)$, where the two gamma matrices can be given by

$$Gamma^1 = begin{pmatrix} 1 & 0 cr 0 & -1 end{pmatrix}$$
and
$$Gamma^2 = begin{pmatrix} 0 & 1 cr 1 & 0 end{pmatrix}.$$

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