One way of constructing groups which are subsets of some ℝn is: Let a be a finite-dimensional real algebra and let G be the group of units in a . We get more groups as subgroups of G . For example, we have used the algebra Mn(ℝ) in which the group of units is GL(n,ℝ) and we have the important subgroup SO(n) . Our groups Spin(k) are subgroups of the group of units in the Clifford algebra Ck .
KeywordsClifford Algebra Center Spin Algebra Homomorphism Closed Manifold Spin Group
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