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).
