Date: 2023-06-02 | Article ID: 08264 |

Article 03910 introduced **Clifford algebra**, which is sometimes also called **geometric algebra**. This article uses Clifford algebra to construct the **spin group**, which is a double cover of the part of the Lorentz group that is generated by pairs of reflections. This is a prerequisite for the idea of a **spinor field**, which is an important ingredient in our current understanding of nature. The construction and basic topological properties of the spin group are explained for arbitrary signatures (p,q) with p+q≥ 2, including euclidean signatures (either p or q is 0), lorentzian signatures (either p or q is 1), and other signatures (p and q are both ≥ 2).

**2023-06-02**(made the abstract more precise)**2023-05-14**(added two footnotes)**2023-05-08**(deleted a paragraph that didn't add any insight, moved a cross-reference)**2023-04-30**(first version)

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